Question

The probability that a dancer likes ballet is .35. The probability that the dancer likes tap is .45. The probability that the dancer likes both ballet and tap is .30.
What is the probability that the dancer likes ballet if we know she likes tap?

.30

.35

.67

.75

Answer 1

It is given the probability that a dancer like ballet is 0.35

So, P(B) = 0.35

It is given the probability that a dancer like tap is 0.45

So, P(T)= 0.45

The probability that he likes both ballet and tap is 0.30

So, $P(B\cap T)=0.30$

the probability that the dancer likes ballet if we know she likes tap. This is the case of conditional probability.

So, $P(B/T)=\frac{P(B\cap T)}{P(T)}$

$P(B/T)=\frac{0.30}{0.45}$

= 0.666

= 0.67

Therefore, the probability that the dancer likes ballet if we know she likes tap is 0.67.

Option 3 is the correct answer.