Question

What is the probability of drawing the compliment of a king or a

queen from a standard deck of playing cards? (3 marks)

Answer 1

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846

Explanation:

Step(i):-

Let 'S' be the sample space associated with the drawing of a card

n (S) = 52C₁ = 52

Let E₁ be the event of the card drawn being a king

`n( E_(1) ) = 4 _{C_(1) } = 4`

Let E₂ be the event of the card drawn being a queen

`n( E_(2) ) = 4 _{C_(1) } = 4`

But E₁ and E₂ are mutually exclusive events

since E₁ U E₂ is the event of drawing a king or a queen

step(ii):-

The probability of drawing of a king or a queen from a standard deck of playing cards

P( E₁ U E₂ ) = P(E₁) +P(E₂)

`= (4)/(52) + (4)/(52)`

P( E₁ U E₂ ) =
`(8)/(52)`

step(iii):-

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards

`P(E_(1)UE_(2)) ^(-) = 1- P(E_(1) U E_(2) )`

`P(E_(1)UE_(2)) ^(-) = 1- (8)/(52)`

`P(E_(1)UE_(2)) ^(-) = (52-8)/(52) = (44)/(52) = 0.846`

Conclusion:-

The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846