Question

If a card is picked at random from a standard 52-card deck, what is the probability of getting a heart or a 8 of clubs? Give your answer as a fraction.

Answer 1

Given:

Number of hearts in deck of cards = 13

Number of 8 of clubs in a deck of cards = 1

Required: Probability of getting a heart or a 8 of clubs

Explanation:

Probability of getting a heart = 13/52

Probability of getting 8 of clubs = 1/52

Use the formula

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Therefore,

`\begin{gathered} P(\text{ a heart or a 8 of clubs\rparen = P\lparen a heart\rparen+P\lparen a 8 of clubs\rparen-P\lparen a heart and a 8 of club\rparen } \\ =(13)/(52)+(1)/(52)-0 \\ =(14)/(52) \\ =(7)/(26) \end{gathered}`

Final Answer: Probability of getting a heart or a 8 of clubs is 7/26.