Question

A biased die is tossed and the respective probabilities for various faces to turn up are given below

Face :	1	2	3	4	5	6
Probability	0.1	0.24	0.19	0.18	0.15	0.14

If an even face has turned up, then the probability that it is face 2 or face 4, is

• A. 0.25
• B. 0.42
• C. 0.75
• D. 0.9

Answer 1

Answer: (C)

0.75

Answer 2

Let $A$ be the event that even face turns up and be the event that it is 2 or 4.

Then $P ( A ) = P ( 2 ) + P ( 4 ) + P ( 6 ) = 0.24 + 0.18 + 0.14 = 0.56$

$P ( B ) = P ( 2 ) + P ( 4 ) = 0.24 + 0.18 = 0.42$

So, $P ( B / A ) = \frac { P ( B \cap A ) } { P ( A ) } = \frac { P ( B ) } { P ( A ) } = \frac { 0.42 } { 0.56 } = 0.75$ .