Question

Solve the next 3 problems:

1) A tool manufacturing plant buys screws from three different suppliers A. B and C. 50% is purchased from B and C in equal parts, while the rest is acquired from A. If the percentage of defective screws for A, B and C is 5%, 10% and 12%, respectively. What is the probability that a defective screw will be sold by B?

2) If two cards are drawn from a conventional 52-card deck, what is the probability that one is an Ace and a figure?

3)What is the maximum value of p for a binomial experiment where for n trials r successes are observed? 3) Which r rites are observed? Check the result obtained when n = 20 and r = 5.

Answer 1

ANS 1

Probability of a screw buy from supplier A, P(A)=50%=0.5
Probability of a screw buy from supplier B, P(B)=25%=0.25
Probability of a screw buy from supplier C, P(C)=25%=0.25

Let defected is D

On the basis of additional information
Given the screw supply by A, probability of it being defective P(D/A)=5%=0.05
Given the screw supply by B, probability of it being defective P(D/B)=10%=0.10
Given the screw supply by C, probability of it being defective P(D/C)=12%=0.12

Given the screw is defective, probability of it being sold by B

P(B/D)=P(B)×P(DB)/[P(B)×P(DB)]+[P(A)×P(DA)]+[P(C)×P(DC)]

(BY BAY’S THEOREM)

=0.25×0.10/ [0.5×0.05]+ [0.25×0.10]+[0.25×0.12]

=0.025/0.065

=0.3846
Given the screw is defective, probability of it being sold by B=0.3846

(2)

ACE =4

FIGURE =52-16 =36

REQUIRED PROBABILITY = [4C1*36C1]/ 52C2 ( 52C2 = 52! / 2!* 50!)

=4*36/ 1326

=0.1086

(3) QUESTION IS MISPRINT