A coin is flipped 54 times, find the probability that the number of flips landing on heads is between 20 and 30 inclusively.
Guide On Rating System
Vote
The probability of getting a certain number of heads in a certain number of flips follows a binomial distribution. 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 in n trials,
- C(n, k) is the number of combinations of n items taken k at a time,
- p is the probability of success on any given trial (in this case, the probability of flipping heads, which is 0.5),
- n is the number of trials (in this case, the number of coin flips, which is 54),
- k is the number of successes (in this case, the number of heads we want to get, which is between 20 and 30).
We need to calculate this probability for each value of k between 20 and 30, and then add up these probabilities to get the total probability.
This calculation can be quite complex, but fortunately, there are statistical software and online calculators that can do it for us. Using such a tool, we find that the probability of getting between 20 and 30 heads (inclusive) in 54 coin flips is approximately 0.629.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99