Question

In a batch of 15 jars of instant coffee, 5 have been under filled. Suppose 6 of these jars are selected without replacement. If more than 1 of these selected jars are under filled, the whole batch is sent back for refill. What is the probability of the batch being sent back for refill?​

Answer 1

Probability of the batch being sent back for refill is 0.0897

Explanation:

The probability of the batch being sent back for refill is equal to the probability of selecting two or more under filled jars out of the six jars selected.

First, we can find the probability of selecting one under filled jar out of the six jars selected:

P(selecting one under filled jar) = (5/15) * (10/14) * (9/13) * (8/12) * (7/11) * (6/10) = 0.0768

Then, we can find the probability of selecting two under filled jars out of the six jars selected:

P(selecting two under filled jars) = (5/15) * (4/14) * (10/13) * (9/12) * (8/11) * (7/10) = 0.0129

Finally, we can add these probabilities together to find the probability of selecting two or more under filled jars:

P(selecting two or more under filled jars) = P(selecting one under filled jar) + P(selecting two under filled jars)

P(selecting two or more under filled jars) = 0.0768 + 0.0129 = 0.0897

Therefore, the probability of the batch being sent back for refill is 0.0897 or approximately 8.97%.