Question

score: 5.67/15 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) an 8 of clubs? b) a spade or diamond? c) an ace or diamond?

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 8 of Clubs

There is only 1 eight - of - clubs in a deck. So $n(A)=1$. Then $P(\text{8 of Clubs})=\frac{1}{52}\approx0.0192$.

Step3: Calculate probability of a Spade or Diamond

There are 13 spades and 13 diamonds. So $n(A)=13 + 13=26$. Then $P(\text{Spade or Diamond})=\frac{26}{52}=0.5000$.

Step4: Calculate probability of an Ace or Diamond

There are 4 aces and 13 diamonds. But the ace of diamonds is counted twice. So $n(A)=4 + 13-1 = 16$. Then $P(\text{Ace or Diamond})=\frac{16}{52}\approx0.3077$.

Answer:

a) 0.0192
b) 0.5000
c) 0.3077