Question

1. a single card is drawn from a deck. what is the probability of selecting a queen or a heart? a. 17/52 b. 4/13 c. 15/52 d. 9/26

Explanation:

Step1: Calculate number of queens

There are 4 queens in a deck of 52 cards. So the probability of drawing a queen, $P(Q)=\frac{4}{52}$.

Step2: Calculate number of hearts

There are 13 hearts in a deck of 52 cards. So the probability of drawing a heart, $P(H)=\frac{13}{52}$.

Step3: Calculate number of queen - of - hearts

There is 1 queen - of - hearts. So the probability of drawing the queen - of - hearts, $P(Q\cap H)=\frac{1}{52}$.

Step4: Use the addition rule of probability

The addition rule for two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here $A$ is the event of drawing a queen and $B$ is the event of drawing a heart. So $P(Q\cup H)=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{4 + 13-1}{52}=\frac{16}{52}=\frac{4}{13}$.

Answer:

b. 4/13