The probability that a dancer likes ballet is .35. The probability that the dancer likes tap is .45. The probability that the da

Question

3 years ago

14

ncer 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

1 answer:

Tom [10] · Answer 1 · 2022-03-09T01:03:45+03:00

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.