A company manufactures caclculators in batchers of 64 and there is a 5% rate of defects. Find the probability of getting exactly three defects in a batch
See, uh, what I replied to the other one and check if that's anywhere close to what you need.
41664(0.05)^3*(0.95)^61= 0.228
To find the probability of getting exactly three defects in a batch, we can use the binomial probability formula. The formula for the probability of getting exactly k successes in n trials, with a probability p of success in each trial, is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
In this case, the company manufactures calculators in batches of 64, and the defect rate is 5% or 0.05. So, we need to calculate P(X = 3) using the given values.
Here's how to calculate the probability step by step:
1. Calculate the combination (n choose k) using the formula (n! / (k! * (n-k)!)). In this case, n = 64 (batch size) and k = 3 (number of defects). So, (64 choose 3) = (64! / (3! * (64-3)!)).
2. Calculate p^k, where p is the probability of success (defect) in each trial. In this case, p = 0.05 (5% defect rate) and k = 3. So, p^k = 0.05^3.
3. Calculate (1 - p)^(n - k), where n is the total number of trials and k is the number of successes (defects) we want. In this case, n = 64 (batch size) and k = 3 (number of defects). So, (1 - p)^(n - k) = (1 - 0.05)^(64 - 3).
4. Multiply the three calculated values from steps 1, 2, and 3 to get the probability of exactly three defects in a batch.
P(X = 3) = (64 choose 3) * (0.05^3) * (0.95^61)
By evaluating the expression, you should get the probability of getting exactly three defects in a batch.