Question

question 5
0/1 pt 2 details
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 hearts?
b) a heart or club?
c) a number smaller than 10 (counting the ace as a 1)?

Explanation:

Step1: Recall probability formula

The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 52$.

Step2: Calculate probability of 8 of Hearts

There is only 1 card that is an 8 of Hearts. So, $n(E)=1$. Then $P(\text{8 of Hearts})=\frac{1}{52}\approx0.0192$.

Step3: Calculate probability of Heart or Club

There are 13 hearts and 13 clubs. So, $n(E)=13 + 13=26$. Then $P(\text{Heart or Club})=\frac{26}{52}=0.5000$.

Step4: Calculate probability of number smaller than 10

Each suit has 9 cards that are smaller than 10 (Ace = 1, 2 - 9). Since there are 4 suits, $n(E)=9\times4 = 36$. Then $P(\text{number}<10)=\frac{36}{52}\approx0.6923$.

Answer:

a) 0.0192
b) 0.5000
c) 0.6923