Question

3 cards are chosen from a 52 card deck. What is the condition probabilty that all the chosen cards are 2's if the first card card drawn is a two? What is one of the chosen cards if the two of hearts? What if at least 1 of the drawn cards is a two?

Answer 1

1)

P(first card is a two) =(4/52)

P(all three are 2's) =(4/52)*(3/51)*(2/50)

therefore P(all are 2's |first card is a two) =P(all three are 2's)/P(first card is a two)

=(4/52)*(3/51)*(2/50)/(4/52)=1/425

2)

P(one of 3 is two of hearts) =C(1,1)*C(51,2)/C(52,3)=1*1275/23426 =3/52

P(one is 2 of hearts and other 2 are from remaining 2's) =C(1,1)*C(3,2)/C(52,3)=1*3/22100=3/22100

P(all are 2's |one of them is  two of hearts) =(3/22100)/(3/52)=1/425

3)

P(at least one card is a two) =1-P(none is of two) =1-C(48,3)/C(52,3)=1-17296/22100=1201/5525

P(all are 2's | at least one card is a two) =(4/52)*(3/51)*(2/50)/(1201/5525) =1/1201