Question

the probability of drawing a blue ball from bag a is $\frac{1}{5}$ and the probability of drawing a red ball from bag b is $\frac{2}{3}$. what is the probability of drawing a blue ball from bag a and a red ball from bag b?

Explanation:

Step1: Use the formula for independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event of drawing a blue ball from Bag \(A\) and \(B\) be the event of drawing a red ball from Bag \(B\).

Step2: Substitute the given probabilities

We know \(P(A)=\frac{1}{5}\) and \(P(B)=\frac{2}{3}\). Then \(P(A\cap B)=\frac{1}{5}\times\frac{2}{3}\).

Step3: Calculate the product

\(\frac{1}{5}\times\frac{2}{3}=\frac{1\times2}{5\times3}=\frac{2}{15}\)

Answer:

\(\frac{2}{15}\)