Question

jenelle draws one from a standard deck of 52 cards. determine the probability of drawing either a jack or a heart. write your answer as a reduced fraction. answer =

Explanation:

Step1: Calculate number of jacks

There are 4 jacks in a deck, so $n(J)=4$.

Step2: Calculate number of hearts

There are 13 hearts in a deck, so $n(H)=13$.

Step3: Calculate number of jack - hearts

There is 1 jack of hearts, so $n(J\cap H) = 1$.

Step4: Use the addition rule of probability

The formula for $P(A\cup B)$ is $P(A)+P(B)-P(A\cap B)$. Here $A$ is the event of drawing a jack and $B$ is the event of drawing a heart. The total number of cards $n(S)=52$. So $P(J\cup H)=\frac{n(J)}{n(S)}+\frac{n(H)}{n(S)}-\frac{n(J\cap H)}{n(S)}=\frac{4 + 13- 1}{52}$.

Step5: Simplify the fraction

$\frac{4 + 13- 1}{52}=\frac{16}{52}=\frac{4}{13}$.

Answer:

$\frac{4}{13}$