Question

For a biased dice, the probability for the different faces to turn up are

Face	1	2	3	4	5	6
P	0.10	0.32	0.21	0.15	0.05	0.17

The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.

Options

• `16/21`

• `1/10`

• `5/16`

• `5/21`

Answer 1

For a biased dice, the probability for the different faces to turn up are

Face	1	2	3	4	5	6
P	0.10	0.32	0.21	0.15	0.05	0.17

The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is `underlinebb(5/21)`.

Explanation:

Let E: ‘face 1 comes up’ and F: ‘face 1 or 2 comes up’

`\implies` E ∩ F = E  ...(∵ E ⊂ F)

∴ P(E) = 0.10 and

P(F) = P(1) + P(2)

= 0.10 + 0.32

= 0.42

Hence, required probability

= `P(E/F)`

= `(P(E ∩ F))/(P(F))`

= `(P(E))/(P(F))`

= `0.10/0.42`

= `5/21`