Question

score: 9/17 answered: 9/17 question 10 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 6 of clubs? b) a spade? c) a number smaller than 4 (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 set and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 52$ (total number of cards in a deck).

Step2: Calculate probability of getting a 6 of Clubs

There is only 1 six - of - clubs in a deck. So $n(E)=1$. Then $P(\text{6 of Clubs})=\frac{1}{52}\approx0.0192$.

Step3: Calculate probability of getting a Spade

There are 13 spades in a deck. So $n(E) = 13$. Then $P(\text{Spade})=\frac{13}{52}=0.2500$.

Step4: Calculate probability of getting a number smaller than 4

The cards with number smaller than 4 (counting ace as 1) are ace, 2, 3. There are 4 aces, 4 twos and 4 threes. So $n(E)=4 + 4+4 = 12$. Then $P(\text{number}<4)=\frac{12}{52}\approx0.2308$.

Answer:

a) 0.0192
b) 0.2500
c) 0.2308