To solve for the probability that exactly 3 out of 5 bulbs chosen are defective, given that
20% of the bulbs are defective, we can use the binomial probability formula. Here's how it's done:
Define the variables:
Total number of trials,
n=5Probability of a defective bulb,
p=20%=‌Probability of a non-defective bulb,
q=1−p=1−‌=‌Calculate the probability:
We need to find the probability of exactly 3 defective bulbs,
P(X=3).
Apply the binomial probability formula:
P(X=3)=‌5C3(‌)3(‌)2Calculate the individual components:
The coefficient,
‌5C3, is the number of ways to choose 3 defective bulbs from 5 . This is calculated as:
‌5C3=‌=‌=10Plug in the values:
‌(‌)3=‌‌(‌)2=‌Calculate the probability:
P(X=3)=10×‌×‌=10×‌=‌=‌Therefore, the probability that exactly 3 out of the 5 bulbs chosen are defective is
‌.