Question

The probability that an individual is​ left-handed is 0.180 In a class of 24 ​students, what is the probability of finding five​ left-handers? Round the answer to the nearest thousandth.

Answer 1

The probability of finding five left-handers in a class of 24 students is approximately 0.043.

Step-by-step explanation:

To find the probability of finding exactly 5 left-handers in a class of 24 students, we can use the binomial probability formula:

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

Where:

P(x) is the probability of finding x left-handers

C(n,x) is the number of ways to choose x left-handers from n students, which can be calculated using combinations (nCx) = n! / (x!(n-x)!)

p is the probability of an individual being left-handed, which is given as 0.180

n is the total number of students, which is 24

x is the number of left-handers we want to find, which is 5

1. Calculate the combination C(24,5): C(24,5) = 24! / (5!(24-5)!) = 4,368
2. Calculate the probability of finding 5 left-handers: P(5) = 4,368 * (0.180)^5 * (1-0.180)^(24-5)
3. Round the answer to the nearest thousandth: P(5) ≈ 0.043

Therefore, the probability of finding five left-handers in a class of 24 students is approximately 0.043.