Question

suppose one card is drawn at random from a standard deck. answer each part. write your answers as fractions. (a) what is the probability that the card drawn is a four? (b) what is the probability that the card drawn is a red card? (c) what is the probability that the card drawn is a four and a red card?

Explanation:

Step1: Determine total number of cards

A standard deck has 52 cards.

Step2: Find number of favorable outcomes for part (a)

There are 4 fours in a deck (one in each suit). Probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(a)=\frac{4}{52}=\frac{1}{13}$.

Step3: Find number of favorable outcomes for part (b)

There are 26 red cards in a deck (13 hearts and 13 diamonds). So $P(b)=\frac{26}{52}=\frac{1}{2}$.

Step4: Find number of favorable outcomes for part (c)

There are 2 red fours (4 of hearts and 4 of diamonds). So $P(c)=\frac{2}{52}=\frac{1}{26}$.

Answer:

(a) $\frac{1}{13}$
(b) $\frac{1}{2}$
(c) $\frac{1}{26}$