Question

score: 6/15 answered: 6/15 question 7 as shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). each suit is split into 13 individual cards (ace, 2 - 10, jack, queen, and king). if you select a card at random, what is the probability of getting: (round to 4 decimal places where possible) a) a 3 of hearts? b) a club or heart? c) an ace or heart?

Explanation:

Step1: Recall probability formula

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes. Here, $n(S) = 52$.

Step2: Calculate probability of 3 of Hearts

There is only 1 three - of - hearts in a deck of 52 cards. So $P(\text{3 of Hearts})=\frac{1}{52}\approx0.0192$.

Step3: Calculate probability of Club or Heart

There are 13 clubs and 13 hearts. Using the formula for the probability of the union of two non - overlapping events $P(A\cup B)=P(A)+P(B)$ (since a card can't be both a club and a heart at the same time), $P(\text{Club or Heart})=\frac{13 + 13}{52}=\frac{26}{52}=0.5000$.

Step4: Calculate probability of Ace or Heart

There are 4 aces and 13 hearts. But the ace of hearts is counted in both groups. So $n(\text{Ace or Heart})=4 + 13-1=16$. Then $P(\text{Ace or Heart})=\frac{16}{52}\approx0.3077$.

Answer:

a) 0.0192
b) 0.5000
c) 0.3077