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

Answer:

a) $P=\frac{1}{221}$

b) $P=\frac{4}{663}$

c) $P=\frac{4}{221}$

Step-by-step 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 $P(T_1)=\frac{4}{52}=\frac{1}{13}$

a) Second card drawn is 10,

Probability of drawn second card 10 is $P(T_2)=\frac{3}{51}=\frac{1}{17}$

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

$P=P(T_1)\times P(T_2)$

$P=\frac{1}{13}\times \frac{1}{17}$

$P=\frac{1}{221}$

b) Second card drawn is Jack,

Probability of drawn second card Jack is $P(J)=\frac{4}{51}$

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

$P=P(T_1)\times P(J)$

$P=\frac{1}{13}\times \frac{4}{51}$

$P=\frac{4}{663}$

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 $P(p)=\frac{12}{51}=\frac{4}{17}$

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

$P=P(T_1)\times P(p)$

$P=\frac{1}{13}\times \frac{4}{17}$

$P=\frac{4}{221}$