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

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]