Question

Sia has seven background dancers for her performace at the Grammys, three of them are wearing black costumes amd four are wearing white costumes. Two of the dancers are selected at random to join Sia onstage for the encore. If at least one of the two is wearing white, what is the probability that at least one is wearing black? If both of them are wearing the same color, what is the probability they are both wearing white?

Answer 1

1) The number of ways in which 2 dancers can be taken is

Now, if at least one one of the two is wearing white, Then the number of possible outcomes remains

Now, out of these 18, outcomes there are number of ways in which both are wearing white

hence the required probability is

(2) Number of ways in which both can wear the same color is

And there are number of ways in which both can wear white

Hence the required probability is