Question

a recent survey shows that 66% of college students have a cat and 37% have a HBO subscription. Assuming these two events are independent, what is the probability that a randomly selected student has neither a cat nor HBO

Answer 1

Answer:

$P(C'\ and\ H') =0. 2178$

Step-by-step explanation:

Let

$C \to$ Student with cat

$H \to$ Student has HBO sub

$P(C) = 66\% \\ P(H) = 37\%$

Required

$P(C'\ and\ H')$

This is calculated as:

$P(C'\ and\ H') = P(C') * P(H')$

Using complement rules, we have:

$P(C'\ and\ H') = [1 - P(C)] * [1 - P(H)]$

So, we have:

$P(C'\ and\ H') = [1 - 66\%] * [1 - 37\%]$

$P(C'\ and\ H') = [33\%] * [66\%]$

$P(C'\ and\ H') =0. 2178$