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:a) [tex]P=\frac{1}{221}[/tex]b) [tex]P=\frac{4}{663}[/tex]c) [tex]P=\frac{4}{221}[/tex]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 [tex]P(T_1)=\frac{4}{52}=\frac{1}{13}[/tex]a) Second card drawn is 10,Probability of drawn second card 10 is [tex]P(T_2)=\frac{3}{51}=\frac{1}{17}[/tex]Total probability that first card was 10 and second card is 10,[tex]P=P(T_1)\times P(T_2)[/tex][tex]P=\frac{1}{13}\times \frac{1}{17}[/tex][tex]P=\frac{1}{221}[/tex]b) Second card drawn is Jack,Probability of drawn second card Jack is [tex]P(J)=\frac{4}{51}[/tex]Total probability that first card was 10 and second card is Jack,[tex]P=P(T_1)\times P(J)[/tex][tex]P=\frac{1}{13}\times \frac{4}{51}[/tex][tex]P=\frac{4}{663}[/tex]c) Second card drawn is picture card,Number of picture card is 4j's, 4Q's, 4K's = 12Probability of drawn second card picture card is [tex]P(p)=\frac{12}{51}=\frac{4}{17}[/tex]Total probability that first card was 10 and second card is picture card,[tex]P=P(T_1)\times P(p)[/tex][tex]P=\frac{1}{13}\times \frac{4}{17}[/tex][tex]P=\frac{4}{221}[/tex]