Question

1. a cat being all black and a cat being female are independent from one another. about 33% of all cats are black. about 50% of cats are female. what is the probability that a randomly selected cat is black and female? 6. a and b are independent events. p(a)=0.35, p(b)=0.15. what is the p(a and b)?

Explanation:

Step1: Recall the formula for independent events

For independent events $A$ and $B$, $P(A\ and\ B)=P(A)\times P(B)$.

Step2: Convert percentages to decimals for the first - part

In the first part, $33\% = 0.33$ (probability of a cat being black) and $50\%=0.5$ (probability of a cat being female). Then $P(A\ and\ B)=0.33\times0.5$.
$0.33\times0.5 = 0.165$.

Step3: Solve the second - part

Given $P(A)=0.35$ and $P(B)=0.15$. Using the formula $P(A\ and\ B)=P(A)\times P(B)$, we have $P(A\ and\ B)=0.35\times0.15$.
$0.35\times0.15 = 0.0525$.

Answer:

1. $0.165$
2. $0.0525$