Question

4.2 theoretical probability. calculating theoretical probabilities (deck of cards). an experiment is to draw 1 card from a fair deck of playing cards. a) if you were to list the sample space, how many equally likely outcomes would it have? b) find the probability of getting a 6. leave your answer as a fraction. c) find the probability of not getting a club. leave your answer as a fraction. d) find the probability of getting a club. leave your answer as a fraction. e) find the probability of getting a 6 or a diamond. leave your answer as a fraction.

Explanation:

Step1: Determine sample - space size

A standard deck of playing cards has 52 cards. So the number of equally - likely outcomes in the sample space is 52.

Step2: Calculate probability of getting a 6

There are 4 cards with the number 6 in a deck (one 6 in each suit). The probability $P(6)$ is the number of favorable outcomes divided by the number of total outcomes. So $P(6)=\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate probability of not getting a club

There are 13 clubs in a deck. The number of non - club cards is $52 - 13=39$. So the probability $P(\text{not club})=\frac{39}{52}=\frac{3}{4}$.

Step4: Calculate probability of getting a club

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

Step5: Calculate probability of getting a 6 or a diamond

There are 4 cards with the number 6 and 13 diamond cards. But the 6 of diamonds is counted twice. So the number of favorable outcomes is $4 + 13-1 = 16$. Then $P(6\text{ or diamond})=\frac{16}{52}=\frac{4}{13}$.

Answer:

a) 52
b) $\frac{1}{13}$
c) $\frac{3}{4}$
d) $\frac{1}{4}$
e) $\frac{4}{13}$