Question

1. what is the probability of drawing each of the following from a standard deck of cards?

a) a red card b) a club c) a 6
d) a face card e) a black ace

Explanation:

Step1: Know deck - card count

A standard deck has 52 cards.

Step2: Calculate probability formula

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step3: Probability of red card

There are 26 red cards (13 hearts + 13 diamonds). So $P(\text{red})=\frac{26}{52}=\frac{1}{2}$.

Step4: Probability of club

There are 13 clubs. So $P(\text{club})=\frac{13}{52}=\frac{1}{4}$.

Step5: Probability of 6

There are 4 cards with number 6 (one in each suit). So $P(6)=\frac{4}{52}=\frac{1}{13}$.

Step6: Probability of face - card

There are 12 face - cards (4 Jacks, 4 Queens, 4 Kings). So $P(\text{face card})=\frac{12}{52}=\frac{3}{13}$.

Step7: Probability of black ace

There are 2 black aces (ace of spades and ace of clubs). So $P(\text{black ace})=\frac{2}{52}=\frac{1}{26}$.

Answer:

a) $\frac{1}{2}$
b) $\frac{1}{4}$
c) $\frac{1}{13}$
d) $\frac{3}{13}$
e) $\frac{1}{26}$