As the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000, what happens to the probability of getting between 40% and 60% heads? What happens to the probability of getting exactly 50% heads?
answer choices
a. Both of those probabilities increase.
b. Both of those probabilities decrease.
c. The first probability increases, but the second one decreases.
d. The first probability decreases, but the second one increases.

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varshamittal029 varshamittal029 · Answer 1 · 2022-12-03T09:59:35-05:00

Option (B) is the correct one.

Both of those probabilities decrease.

Given, the number of tosses of a fair coin goes up from 10, to 100, to 1,000 and to 10,000.

we have to find the effect on the probability of getting exactly 50% heads.

In 10 tosses,

we have to get heads 5 times,

P(X = 5) = (1/2)^5(1/2)^5

P(X = 5) = (1/2)^10

In 100 tosses,

we have to get heads 50 times,

P(X = 50) = (1/2)^50(1/2)^50

P(X = 50) = (1/2)^100

and so on.

It is clear that the probability of getting 50% heads decreases.

Also, Probability of getting heads between 40% and 60% decreases.

Hence, both of those probabilities decrease.

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