Question
Jan Villaroel
Topic: Probability Posted 5 months ago
A coin is flipped 54 times, find the probability that more than 20 of the flips landed on heads.

A coin is flipped 54 times, find the probability that more than 20 of the flips landed on heads.


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Koala Tutor
Jul 5, 2024
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The probability of getting more than 20 heads in 54 flips is the sum of the probabilities of getting 21, 22, ..., 54 heads.

This is a binomial distribution problem, where the number of trials is 54, the probability of success (getting a head) on each trial is 0.5, and we want to find the probability of getting more than 20 successes.

The formula for the binomial distribution is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where:
- P(X=k) is the probability of getting k successes,
- C(n, k) is the number of combinations of n items taken k at a time,
- p is the probability of success on each trial,
- n is the number of trials,
- k is the number of successes.

To find the probability of getting more than 20 heads, we need to sum up the probabilities of getting 21, 22, ..., 54 heads.

P(X>20) = P(X=21) + P(X=22) + ... + P(X=54)

Calculating this manually would be very tedious and time-consuming. However, we can use statistical software or a calculator with binomial distribution functions to find the answer.

Using a statistical software or calculator, we find that the probability of getting more than 20 heads in 54 flips is approximately 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

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