Question

Each of three identical jewelry boxes has two drawers. In each drawer of the first box there is a gold watch. In each drawer of the second box there is a silver watch. If we select a box at random, open one of the drawers and find it to contain a silver watch, what is the probability that the other drawer has the gold watch? Explain every step clearly

Answer 1

Answer:

Step-by-step explanation:

Step 1:

Let E1,E2E1,E2 and E3E3 be the event that boxes I,II and III are chosen respectively.

The P(E1)=P(E2)=P(E3)=13P(E1)=P(E2)=P(E3)=13

Consider the occurrence A as the occurrence that the watch drawn in of gold.

Then P(A/E1)P(A/E1)=P(a gold watch from box I)=2222=1

P(A/E2)P(A/E2)=P(a gold watch from box II)=0

P(A/E3)P(A/E3)=P(a gold watch from box III)=12

Step 2:

The probability that the other watch in the box is of gold=the probability that gold watch is drawn from the box I

⇒P(E1/A)⇒P(E1/A)

By Baye's theorem ,we know that

P(E1/A)=P(E1)P(A/E1)P(E1).P(A/E1)+P(E2)P(A/E2)+P(E3)P(A/E3)P(E1/A)=P(E1)P(A/E1)P(E1).P(A/E1)+P(E2)P(A/E2)+P(E3)P(A/E3)

⇒1/3×11/3×1+1/3×0+1/3×1/2

⇒2/3

Hence the required probability is 2/3

hope this is helpful