Answer:
a) 10*0.51^3*0.49^2=approx 0.32
b)1-0.49^5= approx 0.97
c)1-0.51^5=0.965
d) approx 0.028 =P(all kids are girls) approx 0.035 =P(all kids are boys)
P(all kids are of the same sexboys or girls)=0.063
Step-by-step explanation:
a) The probability that exactly 3 of 5 kids are boys is
p(3 boys)=C5 3 *p^3*q^2
C5 3 = 5!/(3!*2!)= 4*5/2=10
p=0.51 is the probability a child is boy
q=1-p=1-0.51=0.49 is the probability a child is girl
P(3 boys of 5 kids)= 10*0.51^3*0.49*2
b) The event that at least 1 kid from five is boy is a combination of events
1 boy -4 girls, 2 boys-3 girls, 3 boys-2 girls, 4 boys-1 girl, 5 boys.
The event " all 5 kids are the girls" is the only event which is not the part of
event " at least 1 kid from five is boy"
So P(at least 1 kid from five is boy)=1 - P(all 5 kids are the girls)
P(all 5 kids are the girls)=0.49^5=approx 0.028
P(at least 1 kid from five is boy)=1-0.028=approx 0.97
c) Similarly like b) P(at least one of five kids is girl)= 1-P(all 5 kids are the boys)
P(all 5 kids are the boys)=0.51^5=approx 0.035
P(at least one of five kids is girl)= 1-0.035=approx=0.965
d) Probability all kids are of the same sex= probability that all kids are the boys+ probability all kids are the girls.
Using b) and c) P(all kids of the same sex)= 0.035+0.028=0.063
