Question

when a card is drawn from a standard deck of 52 cards, what is the probability of getting a. queen b.a red. c.a queen or a red card​

Answer 1

(a) Probability of getting a queen from a deck of 52 cards =
`(1)/(13)`

(b) Probability of getting a red card from a deck of 52 cards =
`(1)/(2)`

(c) Probability of getting a queen or a red card from a deck of 52 cards =
`(7)/(13)`

Solution:

Given that card is drawn from a standard deck of 52 cards.

Need to determine probability of getting

(a) queen (b) red (c) a queen or a red card

`\text { Probability of an event }=\frac{\text { favorable number of events }}{\text { total number of events }}`

(a) Calculating probability of getting a queen from a deck of 52 cards

Favorable events are getting a queen of spade, heart , diamond or club.

Means number of favorable events = 4

Total events is all possible outcomes from 52 cards

So Total number of event = 52

`\Rightarrow \text { probability of getting a queen }=(4)/(52)=(1)/(13)`

(b) Calculating probability of getting a red card from a deck of 52 cards

Number of red cards are 13 cards of diamonds and 13 cards of heart = 13+13 =26

So number of favorable event = 26

Total number of event = 52

`\Rightarrow \text { probability of getting a red card }=(26)/(52)=(1)/(2)`

(c) Calculating probability of getting a queen or red card from a deck of 52 cards

Favorable events are 26 red cards + two queens of spade and club. Need to keep in mind that queens of heart and diamond is already considered in 26 red cards.

So number of favorable event = (26+2) = 28

Total number of event = 52

`\text { Probability of getting a queen or red card }=(28)/(52)=(7)/(13)`

Summarizing the result :

(a) Probability of getting a queen from a deck of 52 cards =
`(1)/(13)`

(b) Probability of getting a red card from a deck of 52 cards =
`(1)/(2)`

(c) Probability of getting a queen or a red card from a deck of 52 cards =
`(7)/(13)`