Question

An experiment consists of drawing one card from a bridge deck. The sample space contains 52 outcomes, one for each of the 52 cards. Suppose we assign a probability of 1 52 to each of the cards. Find the probability that the following happens. (a) A queen is drawn. (b) The card drawn is a king or a queen. (c) The card drawn is a heart. (d) The card drawn is a red card.

Answer 1

Answer: a)
`(1)/(13)`

b)
`(2)/(13)`

c)
`(1)/(4)`

d)
`(1)/(2)`

Explanation:

Formula for probability =
`\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}`

The total number of cards in a deck = 52

a) Number of cards having queen =4

Then the probability that a queen is drawn =
`\frac{\text{No. of cards having queen}}{\text{Total cards}}`

`=(4)/(52)=(1)/(13)`

c) Number of cards having King= 4

Then , the number of cards having a queen or king =4+4=8

Then the probability that a king or queen is drawn =
`\frac{\text{No. of cards having king or a queen}}{\text{Total cards}}`

`=(8)/(52)=(2)/(13)`

c) Number of cards having heart = 13

Then the probability that a heart is drawn =
`\frac{\text{No. of cards having heart}}{\text{Total cards}}`

`=(13)/(52)=(1)/(4)`

d) Number of red cards = 26

Then the probability that a red card is drawn =
`\frac{\text{No. of red cards}}{\text{Total cards}}`

`=(26)/(52)=(1)/(2)`