Question

if a single card is drawn from a standard 52 - card deck, what is the probability that it is either a ten or a heart?
a. $\frac{7}{26}$
b. $\frac{3}{13}$
c. $\frac{17}{52}$
d. $\frac{4}{13}$

Explanation:

Step1: Calculate the number of tens

There are 4 tens in a deck.

Step2: Calculate the number of hearts

There are 13 hearts in a deck.

Step3: Calculate the number of ten - of - hearts

There is 1 ten - of - hearts (it was counted in both the tens and the hearts, so we need to subtract the overlap once).

Step4: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

The number of favorable outcomes \(n = 4 + 13-1=16\). The total number of outcomes \(N = 52\). So the probability \(P=\frac{16}{52}=\frac{4}{13}\)

Answer:

D. \(\frac{4}{13}\)