Question

You have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the die until you get a B. What is the probability that the first B appears on the first or the second roll?

A. .333
B. .704
C. .556
D. .037
E. .296

Answer 1

C. .556

Explanation:

Given that you have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the die until you get a B.

Probability of getting A =
`(3)/(6)`

Probability of getting B =
`(2)/(6)`

Probability of getting c =
`(1)/(6)`

Each throw is independent of the other

the probability that the first B appears on the first or the second roll

= P(B) in I throw +P(B) in II throw

= P(B) in I throw + P(either A or C) in I throw*P(B) in II throw

=
`(2)/(6)+(4)/(6)*(2)/(6)\\=(5)/(9) \\=0.556`

Option c is right