Question

events a and b are independent. p(a) = 3/5, and p(b) = 7/15. what is p(a and b)? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Recall the formula for independent events

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

Step2: Substitute the given probabilities

We have $P(A)=\frac{3}{5}$ and $P(B)=\frac{7}{15}$, so $P(A\cap B)=\frac{3}{5}\times\frac{7}{15}$.

Step3: Calculate the product

$\frac{3}{5}\times\frac{7}{15}=\frac{3\times7}{5\times15}=\frac{21}{75}=\frac{7}{25}= 0.28$.

Answer:

$\frac{7}{25}$ or $0.28$