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________.

1. approach 0.5
2. be equal to 0.5
3. be greater than 0.5
4. be less than 0.5

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.