Question

a recent survey shows that 16% of college students have dogs and 38% have an HBO subscription. assuming these two events are independent, what is the probability that a randomly selected college student has neither a dog nor HBO

Answer 1

Answer: $0.939\ or\ 93.9\%$

Step-by-step explanation:

Given

Survey shows that 16% of college students have dogs and 38% have HBO subscription

Probability that a random person have both is

$\Rightarrow P_o=0.16\times 0.38\quad [\text{As both events are independent}]\\\Rightarrow P_o=0.0608$

The probability that the random person has neither of the two is

$\Rightarrow P=1-P_o\\\Rightarrow P=1-0.0608\\\Rightarrow P=0.939$