Question

4. Two cards are selected from a regular deck of cards. If the first was a ten, determine the probability that the second was a (a) ten, (b) jack, (c) picture card 3/K 4CL

Answer 1

a)
`P=(1)/(221)`

b)
`P=(4)/(663)`

c)
`P=(4)/(221)`

Explanation:

Given : Two cards are selected from a regular deck of cards. If the first was a ten.

To determine : The probability that the second was a (a) ten, (b) jack, (c) picture card ?

Solution :

Total number of cards = 52 in which there are 4 sets of 13 cards with two different color.

We are drawing two card one after another without replacement.

Probability of drawn first card 10 is
`P(T_1)=(4)/(52)=(1)/(13)`

a) Second card drawn is 10,

Probability of drawn second card 10 is
`P(T_2)=(3)/(51)=(1)/(17)`

Total probability that first card was 10 and second card is 10,

`P=P(T_1)* P(T_2)`

`P=(1)/(13)* (1)/(17)`

`P=(1)/(221)`

b) Second card drawn is Jack,

Probability of drawn second card Jack is
`P(J)=(4)/(51)`

Total probability that first card was 10 and second card is Jack,

`P=P(T_1)* P(J)`

`P=(1)/(13)* (4)/(51)`

`P=(4)/(663)`

c) Second card drawn is picture card,

Number of picture card is 4j's, 4Q's, 4K's = 12

Probability of drawn second card picture card is
`P(p)=(12)/(51)=(4)/(17)`

Total probability that first card was 10 and second card is picture card,

`P=P(T_1)* P(p)`

`P=(1)/(13)* (4)/(17)`

`P=(4)/(221)`