Discussion

Explanation:

X, Y and Z are events such that

X is the event that the card drawn is black or a king.

Y is the event that the card drawn is a club or a heart or a jack.

Z is the event that the card drawn is an ace or a diamond or a queen.

Consider X.

A black card can be drawn in 26 ways. A king can be drawn in 4 ways. A black king can be drawn in 2 ways.

∴ P(X) = $\frac{26}{52}$ + $\frac{4}{52}$ - $\frac{2}{52}$

∴ P(X) = $\frac{28}{52}$

Consider Y.

A club can be drawn in 13 ways. A heart can be drawn in 13 ways. A jack can be drawn in 4 ways. A Jack of hearts can be drawn in 1 way and a jack of club can be drawn in 1 way.

∴ P(X) = $\frac{13}{52}$ + $\frac{13}{52}$ + $\frac{4}{52}$ - $\frac{1}{52}$ - $\frac{1}{52}$

∴ P(Y) = $\frac{28}{52}$

Consider Z.

An ace can be drawn in 4 ways. A queen can be drawn in 4 ways and a diamond can be drawn in 13 ways. Queen of Diamonds can be drawn in 1 way and ace of diamonds can be drawn in 1 way.

∴ P(Z) = $\frac{4}{52}$ + $\frac{4}{52}$ + $\frac{13}{52}$ - $\frac{1}{52}$ - $\frac{1}{52}$

∴ P(Z) = $\frac{19}{52}$

∴ P(X) = P(Y) > P(Z)

Hence, option (c).

» Your doubt will be displayed only after approval.