Three cards are drawn in succession without replacement from

Three cards are drawn in succession, without replacement, from an ordinary deck of playing cards. Find the probability that the following event occurs: the first card is a black jack; the second card is a 10 or an ace; and the third card is greater than 2 but less than 8

Solution

There are 52 cards in an ordinary playing cards deck

No. of black colored jacks = 2

The probability of drawing a black jack = 2/52

Now there are 51 cards left.

No.of Aces and 10s in the deck = 2 x 4 = 8

Probability of drawing a 10 or an ace = 8 / 51

Now here are 50 cards left in the deck.

The cards, greater than 2 but less than 8 are : 3,4,5,6,7

Total number of such cards = 5 x 4 = 20

Probability of drawing such a card = 20 / 50

Thus, the overall probability = 2/52 x 8/51 x 20/50

= 8 / 3315

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