Respuesta :
Answer:
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846
Step-by-step 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
[tex]n( E_{1} ) = 4 _{C_{1} } = 4[/tex]
Let E₂ be the event of the card drawn being a queen
[tex]n( E_{2} ) = 4 _{C_{1} } = 4[/tex]
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)
[tex]= \frac{4}{52} + \frac{4}{52}[/tex]
P( E₁ U E₂ ) = [tex]\frac{8}{52}[/tex]
step(iii):-
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards
[tex]P(E_{1}UE_{2}) ^{-} = 1- P(E_{1} U E_{2} )[/tex]
[tex]P(E_{1}UE_{2}) ^{-} = 1- \frac{8}{52}[/tex]
[tex]P(E_{1}UE_{2}) ^{-} = \frac{52-8}{52} = \frac{44}{52} = 0.846[/tex]
Conclusion:-
The probability of drawing the compliment of a king or a queen from a standard deck of playing cards = 0.846
