Question

Marsha is playing a game with a set of cards numbered 1 through 10. What is the probability that Marsha will select a card with an odd number on it, replace it back into the deck, and then pick a card that has a value larger than 3?

Answer 1

Let:

A = Pick a card with an odd number

B = Pick a card that has a value larger than 3

N = Total number of cards

so:

$\begin{gathered} P(A)=\frac{5}{N}=\frac{5}{10}=\frac{1}{2} \\ P(B)=\frac{7}{N}=\frac{7}{10} \end{gathered}$

Since they are independent events:

$\begin{gathered} P(A\cap B)=P(A)\cdot P(B) \\ P(A\cap B)=\frac{1}{2}\cdot\frac{7}{10}=\frac{7}{20}=0.35 \end{gathered}$

Answer:

35%