Question

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 (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 10 of diamonds? b) a club? c) a number smaller than 7 (counting the ace as a 1)?

Explanation:

Step1: Determine total number of cards

The total number of cards in a standard deck is 52.

Step2: Calculate number of favorable outcomes for part a

There is only 1 ten - of - diamonds in a deck. So the number of favorable outcomes for getting a 10 of diamonds is 1. The probability $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{52}\approx0.0192$.

Step3: Calculate number of favorable outcomes for part b

There are 13 clubs in a deck. So the probability of getting a club is $P(B)=\frac{13}{52}=\frac{1}{4} = 0.2500$.

Step4: Calculate number of favorable outcomes for part c

The numbers smaller than 7 (counting ace as 1) are ace, 2, 3, 4, 5, 6. There are 4 suits, so the number of such cards is $6\times4 = 24$. The probability of getting a number smaller than 7 is $P(C)=\frac{24}{52}=\frac{6}{13}\approx0.4615$.

Answer:

a. 0.0192
b. 0.2500
c. 0.4615