give the probability............

Question

Write each as a set and then give the probability, of the following happening?
a) From a full pack of picture cards (J,Q,K,A) an ace is dealt?
b) From a set of a single die that a 4 is rolled?
c) From the birth of quadruplets 2boys and 2 girls are born?

Answer 1

a)  Probability (Ace drawn from a full pack) = 4/52 = 1/13

 

 

b) Pr( drawing 4 out of rolling a die) = 1/6

 

 

c)  C ₂ ⁴  ( 1/2) ^2 ( 1/2 ) ^2 =

 

      4! / (2! * 2! ) (1/2) ^4 = 6/ 16 = 3 /8

 

     There are  4 ^2 = 16  possible ways of outcome to be different combination of boys and girls.

 

    { bbbb, bbbg, bbgb, bbgg, bgbb, bgbg, gbbg , gbbb , bggg, gbbg ,gbgb, gbgg, ggbb,gggb,gggg}

 

 You  see  that there are six cases marked italic are total number of cases that outcome appears as 2boys and 2 girls. the probability is 6/16 = 3/8 , exactly like flipping coin 4 times

possible cases where 2 heads and 2 tails appear.