You are dealt a hand of three cards, one at a time. Find the probability of each of the following. a) The first club you get is the third card dealt. b) Your cards are all black. c) You get no hearts. d) You have at least one red card.
Accepted Solution
A:
Answer:a)P=0.145b)P=0.116c)P=0.413d)P=0.884Step-by-step explanation:We know that Total number of cars is 52 .26 red and 26 is black.13 are hearts ,13 are diamonds,13 are clubs,13 are spades.a)Probability P (first club get is the third card dealt)=P(Non-club x Non club x club)So [tex]P=\dfrac{39}{52}\times \dfrac{38}{51}\times \dfrac{13}{50}[/tex] P=0.145b)[tex]P( all\ are\ black)=\dfrac{26}{52}\times \dfrac{25}{51}\times \dfrac{24}{50}[/tex]P=0.116c)[tex]P( no\ heart)=\dfrac{39}{52}\times \dfrac{38}{51}\times \dfrac{37}{50}[/tex]P=0.413d)[tex]P( at\ least\ one red)=1-P(no\ red)[/tex][tex]P(no\ red)=\dfrac{26}{52}\times \dfrac{25}{51}\times \dfrac{24}{50}[/tex][tex]P(no\ red)=0.116[/tex][tex]P( at\ least\ one red)=1-0.116[/tex][tex]P( at\ least\ one\ red)=0.884[/tex]