Lidsney inspected shipments of applices. She inspected 3 from a batch of 140 . If she finds 3 with defects the entire lot is rejected. If max knows knows that 9 of her appliances have minor defects. Find the probability that lidya will reject max shipment of appliances.

To find the probability that Lidya will reject Max's shipment of appliances, we need to calculate the probability of finding 3 or more defective appliances in the batch.

First, let's determine the probability of finding exactly 3 defective appliances in the batch. We can use the binomial probability formula for this:

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

Where:
- P(X = k) is the probability of getting exactly k successes (in this case, defective appliances)
- C(n, k) is the number of combinations of n items taken k at a time (n is the total number of appliances and k is the number of defective appliances)
- p is the probability of each individual appliance being defective
- n is the total number of appliances in the batch

From the given information, we know that Lidya inspected 3 appliances out of a batch of 140, and if she finds 3 with defects, the entire lot is rejected. Also, Max knows that 9 of his appliances have minor defects.

Since Lidya inspected only 3 appliances, we need to consider the probability of finding 3 defective appliances in the remaining 137 untested appliances. The total number of defective appliances can be calculated by subtracting the 9 appliances with minor defects from the total of 140 appliances.

Let's calculate the probability of finding exactly 3 defective appliances:

n = 137 (the number of untested appliances remaining)
k = 3 (the number of defective appliances)
p = (total defective appliances) / (total appliances) = (9) / (140)
C(n, k) = n! / (k! * (n - k)!)

Using these values, we can calculate the probability:

P(X = 3) = C(137, 3) * ((9/140)^3) * ((1 - 9/140)^(137 - 3))

After calculating this probability, we can determine if it is greater than or equal to the threshold for rejection. If the probability is less than the threshold, Lidya will not reject the shipment. If the probability is greater than or equal to the threshold, Lidya will reject the shipment.