Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 175 boxes, each box containing 30 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 8 keyboards from that box. The shipment is accepted if not more than 1 of the 8 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 9 defective keyboards.
Round your answers to four decimal places.
a. What is the probability that this shipment will be accepted?
b. What is the probability that this shipment will not be accepted?
a. 0.214 b. 0.787
please snd answer
To find the probabilities, we need to calculate the probability of selecting not more than 1 defective keyboard from the 8 randomly selected keyboards. Let's break down the problem step by step.
a. What is the probability that this shipment will be accepted?
To calculate this probability, we need to consider two cases:
Case 1: Selecting 0 defective keyboards:
The probability of selecting a non-defective keyboard from the box is (30 - 9) / 30 = 21 / 30.
The probability of selecting 8 non-defective keyboards from the 8 randomly selected keyboards can be calculated by multiplying the probabilities together: (21/30)^8.
Case 2: Selecting 1 defective keyboard:
The probability of selecting a defective keyboard from the box is 9 / 30.
The probability of selecting 7 non-defective keyboards from the remaining 7 keyboards can be calculated by multiplying the probabilities together: (21/30)^7.
Since we want to find the probability of not more than 1 defective keyboard, we can add the probabilities of the two cases together:
P(accept) = (21/30)^8 + 8 * (9/30) * (21/30)^7.
Now let's calculate the probability:
P(accept) = (21/30)^8 + 8 * (9/30) * (21/30)^7
= 0.1022 + 8 * 0.0918
= 0.8836
Therefore, the probability that this shipment will be accepted is 0.8836.
b. What is the probability that this shipment will not be accepted?
The probability of not accepting the shipment is the complement of accepting it, so:
P(not accept) = 1 - P(accept)
= 1 - 0.8836
= 0.1164
Therefore, the probability that this shipment will not be accepted is 0.1164.