Question

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting a heart or diamond. ​(b) Compute the probability of randomly selecting a heart or diamond or spade. ​(c) Compute the probability of randomly selecting a ten or spade.

Answer 1

a) 0.5

b) 0.75

c) 0.307

Explanation:

We are given the following information in the question:

Number of cards in a deck = 52

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

a) P(Heart or Diamond)

Total number of hearts and diamonds in a deck = 13 + 13 = 26

P( Heart or Diamond) =

`\displaystyle(26)/(52) = \displaystyle(1)/(2) = 0.5`

b) P(Heart or Diamond or Spade)

Total number of hearts, diamonds and spades in a deck = 13 + 13 + 13 = 39

P( Heart or Diamond or Spades) =

`\displaystyle(39)/(52) = \displaystyle(3)/(4) = 0.75`

c) P(10 or Spades)

Total number of spades in a deck = 13

Number of 10 in a deck = 4

P( 10 or Spades) =

`\displaystyle(13 + 4 -1)/(52) = \displaystyle(16)/(52) = \displaystyle(4)/(13) = 0.307`