Question

A shipment of 30 inexpensive digital watches, including 10 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected? 

The probability the shipment will be rejected is _______ . 

(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)

Answer 1

30 Shipment of Including watches 10 inexpensive digital Wat Ches that are defective testing randomlig taken 10 for No. of watches are not defective = 30-10 220 No. of Samples of Watches 30c10 To 30045015 No. of Samples that denot have any defective player 20 c16 - 184756 30 C10 12 1- 184756 30045015 2000 = (- 000615 0.99385 Probability the she shipment will be rejected is 0.99

Answer 2

[REMOVED]

Answer 3

SOLUTION :

In the lot of 30 watches 10 are defective.

So, 20 out of 30 are not defective.

P ( No defective in the randomly  chosen 10 out of 30 ) (without replacement)

= 20/30 * 19/29 * …… and so on ….. * 11/21

= (20! / 10!) / (30! / 20!)

= (20! * 20!) / (30! * 10!)

= 0.0061493 

So, 

P( rejecting the lot)

= P(1 or more defective in 10 chosen out of 30)

= 1 - P (No defective in 10 chosen out of 30)

= 1 - 0.0061493

= 0.9938507 

= 0.99 (to two decimal places) 

So, Probability of rejecting the lot is 0.99  (ANSWER).