Probability

[Bhandaripreeti]

A minidisk player is loaded with only rock, jazz, and opera songs. If the probability of 3 rock songs playing in a row is the same as the probability of 2 jazz songs playing in a row, what is the probability that the first 2 songs played will be an opera song and a rock song?

1/64

1/32

5/64

1/9

5/32

[samirpandeyit62]

Preeti, are u sure that there is no data missing in the question, also it would be good if u can post the source of this question.

[ipt20072007]

I would guess that the prob. of choosing a rock song is 1/4 and the probably of choosing a jazz song is 1/8. Thus, the probably of choosing an opera song would be (1 - 3/8) or 5/8.

Hence, the probability of choosing an opera song then a rock song would be 5/8 X 1/4 or 1/32. Of course, this question does not clarify whether the order must be an opera song then a rock song. If order did not matter, however, the answer would be 2/32 or 1/16, but that choice is not available.

Can someone post the OA?

Thanks,

J

[kajcha]

How did you derive that probability of rock song is 1/4?

[ipt20072007]

This was my logic

3 rock songs in a row = 2 jazz songs in a row

(1/a)(1/a)(1/a) = (1/b)(1/b)

1/a^3 = 1/b^2

(1/4)(1/4)(1/4) = (1/8)(1/8) or 1/64 = 1/64

Does that make sense?

J

[kajcha]

not really...

suppose there are r - rock songs, j - jazza songs and o - opera songs

total = r+j+o = x

so probabilty of rock songs = r/x.

I am not getting why are you just choosing 1/a. (Assuming a is the no of rock songs)