Question

A card is dealt from a complete deck of fifty-two playing cards (no jokers). Use probability rules (when appropriate) to find the probability that the card is as stated. (Count an ace as high. Enter your answers as fractions.)

(a) under a 4


(b) above an 8


(c) both under a 4 and above an 8


(d) either under a 4 or above an 8

Answer 1

1 card is drawn from 52 cards .

a. Here we are counting ace as high card. So under 4 there is only two numbers . 2 and 3 .

There is 4 cards with number 2 and 4 cards with number 3 in a deck. So number of cards under a 4 is = 4+4 = 8

So, probability of under a 4 = = 0.15385

b. Above an 8 there is numbers 9,10,J,Q,K and A . each has 4 cards in a deck .

So Total number of cards above 8 is = 4×6 = 24

Probability of above an 8 = = 0.46154

c. Both under a 4 and above an 8 .

This can't be happen. Because we can't get a card which is below 4 and above 8 at the same time . This two events are disjoint . So Probability of this event is 0

Probability of under a 4 and above an 8 = 0

d. P[either under a 4 or above an 8]

= P[under a 4] + P[above an 8]  

= = 0.61538

As this two events are disjoint we can take the individual sum .