Question

There are 20 tiles in a bag. Of these, 9 are purple, 5 are black and the rest are white.

Event A= drawing a white tile on the first draw

Event B= drawing a Black tile on the second draw

If two tiles are drawn from the bag one after the other not replaced, what is P(B|A) expressed in simplest form?

A. 1/4

B. 5/19

C. 3/10

D. 9/20

Answer 1

B

Explanation:

Answer 2

`P(B|A)=(P(A\cap B))/(P(A))\\\\ |\Omega|=20\cdot19=380\\ |A|=6\cdot19=114\\ |A\cap B|=6\cdot5=30\\\\ P(A)=(114)/(380)=(3)/(10)\\ P(A \cap B)=(30)/(380)=(3)/(38)\\\\ P(B|A)=((3)/(38))/((3)/(10))\\\\ P(B|A)=(3)/(38)\cdot(10)/(3)=(5)/(19)\Rightarrow \text{B}`