Question

There are 4 suits (heart, diamond, clover, and spade) in a 52-card deck, and each suit has 13 cards. Suppose your experiment is to draw one card from a deck and observe what suit it is. Express the probability in fraction format. (Show all work. Just the answer, without supporting work, will receive no credit.)

Answer 1

The probability of drawing a heart or diamond is 1/2 or 0.5

The probability that the card is not a spade is 3/4 or 0.75

Explanation:

Consider the provided information.

Part (a) Find the probability of drawing a heart or diamond.

There are 13 cards of heart and 13 cards of diamond.

We need to find the probability of drawing a heart or diamond.

`P(\text{Heart or Diamond})=P(\text{Heart card Drawn})+P(\text{Diamond card Drawn})`

`P(\text{Heart or Diamond})=(13)/(52)+(13)/(52)`

`P(\text{Heart or Diamond})=(26)/(52)=(1)/(2)=0.5`

Hence, the probability of drawing a heart or diamond is 1/2 or 0.5

(b) Find the probability that the card is not a spade.

Out of 52 cards 13 are spade,

That means 52 - 13 = 39 cards are not a spade.

`P(\text{Not spade})=(39)/(52)=(3)/(4)=0.75`

Hence, the probability that the card is not a spade is 3/4 or 0.75