PROBLEM 4E

Two cards are drawn successively and without replacement from an ordinary deck of playing cards. Compute the probability of drawing

(a) Two hearts.

(b) A heart on the first draw and a club on the second draw.

(c) A heart on the first draw and an ace on the second draw.

Hint: In part (c), note that a heart can be drawn by getting the ace of hearts or one of the other 12 hearts.

Answer:

Step 1 of 4:

Given that, two cards are drawn successively and without replacement from an ordinary deck of playing cards.

Step 2 of 4:

a). The aim is to compute the probability of drawing two hearts.

Here ‘H’ denotes ‘heart’ and then by multiplication rule we have,

P( two hearts) = P(HH)

=

=

Conclusion:

Therefore, the probability of drawing two hearts is .