SECTION – 1

10. A card is drawn at random from a well shuffled pack of 52 cards.

X: The card drawn is black or a king

Y: The card drawn is a club or a heart or a jack.

Z: The card drawn is an ace or a diamond or a queen.

Then which of the following is correct?

A. P(X) > P(Y) > P(Z) B. P(X) > = P(Y) = P(Z)

C. P(X) = P(Y) > P(Z) D. P(X) = P(Y) = P(Z)

Solution:

The probability of drawing a black card is P (B) =

The probability of drawing a king card is P(K) =

The probability of drawing a black king is P(B Ç K) =

The probability of drawing a black card or king is

P(X) = P(B È K) = P(B) + P(K) - P(B Ç K)

=

The probability of drawing (a club or heart or Jack)

= P(drawing club) + P(drawing heart) + P(drawing Jack) - P(drawing heart Jack) - P(drawing club Jack)

=

The probability of drawing a ace or diamond or queen P(Z) = P(drawing ace) + P(drawing diamond) + P(drawing queen) - P(drawing diamond queen) - P(drawing diamond ace)

=

P(Z) =

\ P(X) = P(Y) > P(Z) Choice (C)