Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________. approach 0.5 be equal to 0.5 be greater than 0.5 be less than 0.5

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Answer 1

Textbook Question

Chapter 5, Problem 1CQ

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________.

approach 0.5
be equal to 0.5
be greater than 0.5
be less than 0.5

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

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1. Differentiate between discrete and continuous random variables, providing examples for each type. 2. Consider a discrete random variable representing the number of patients visiting a clinic each day. The probabilities for the number of visits are as follows: 0 visits: P(0) = 0.2 1 visit: P(1) = 0.3 2 visits: P(2) = 0.5 Using this information, calculate the expected value (mean) of the number of patient visits per day. Show all your workings clearly. Rubric to follow Definition of Random variables ( clearly and accurately differentiate between discrete and continuous random variables with appropriate examples for each) Identification of discrete random variable (correctly identifies "number of patient visits" as a discrete random variable and explains reasoning clearly.) Calculation of probabilities (uses the probabilities correctly in the calculation, showing all steps clearly and logically) Expected value calculation (calculate the expected value (mean)…

Answer 2

Textbook Question

Chapter 5, Problem 1CQ

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________.

approach 0.5
be equal to 0.5
be greater than 0.5
be less than 0.5

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

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Answer 3

Textbook Question

Chapter 5, Problem 1CQ

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________.

approach 0.5
be equal to 0.5
be greater than 0.5
be less than 0.5

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 5, Problem 1CQ

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________.

approach 0.5
be equal to 0.5
be greater than 0.5
be less than 0.5

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

Answer 8

Expert Solution & Answer

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To fill: The blank in the statement “The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will_________.”

Answer 12

Answer to Problem 1CQ

The probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Answer 13

Explanation of Solution

It is given that the probability that a fair coin lands heads is 0.5 .

According to law of large numbers, the probability is the ratio of favorable outcomes and the total number of outcomes takes place.

Now, law of large numbers defines as the principal of probability that states the same frequency of average outcome of the events on large number of trials. If any of the events are repeating many of the times then on an average it will give same number of outcomes.

Here, a coin is toss repeatedly; the proportion of times it lands head will be same 0.5.

Therefore,the probability that a fair coin lands heads is 0.5 . Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands head will approach 0.5.

Thus, option (i) is correct.

Answer 14

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we toss a coin repeatedly, the proportion of times it lands heads will________. approach 0.5 be equal to 0.5 be greater than 0.5 be less than 0.5

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