Chapter 4, 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 ______.

1. i. approach 0.5
2. ii. be equal to 0.5
3. iii. be greater than 0.5
4. iv. be less than 0.5

To determine

Identify the proportion of times the die lands heads.

Answer to Problem 1CQ

The correct answer is (i), approaches 0.5.

Explanation of Solution

The given information is that the probability that a fair coin lands heads is 0.5. The coin is tossed repeatedly.

Law of large numbers:

If the probability experiment repeats a large number of times then the proportion that a given event occurs will approaches to its probability.

Reason for correct answer:

Here, the probability that a fair coin lands heads is 0.5.

By law of large numbers, if one tosses a coin large number of times the proportion of times it lands heads approaches to its probability. Therefore, the proportion of times the coin lands heads approaches to 0.5.

Therefore, the option approaches 0.5 represents correct answer.

Reason for incorrect answer:

By law of large numbers, the proportion of times the coin lands heads approaches to 0.5 not equal to 0.5, not greater than 0.5 and not less than 0.5.

Thus, the option (ii),(iii), and (iv)  are incorrect.

Hence, the correct answer is (i). approaches 0.5.