# in a family of three children what is the probability of at least one boy child

noogler
489 Points
8 years ago
no. of chances that a child is a boy=1
total no. of chances=2 (boy + girl)
probability that a child was a boy=p=1/2
probability that a chid is not a boy or it is a girl =q=1-p=1/2
as no. of children,n=3

req probaility=P(x=1)=nC1q2p1
[P(x=r)= nCrqn-rpr]

req probability=3/8
Manderaj
18 Points
8 years ago
The sample event for 3 children can be written as
BBB, BBG, BGB,GBB,GGB,GBG,BGG,GGG
Since the question demands atleast 1 boy child we see that the probability is 7/8

THEREFORE THE REQUIRED PROBABILTY IS 7/8

noogler
489 Points
8 years ago
sorry i didnt read question completely
rrequired probability =P(x>=1)=1-P(x=0)=1-3C0(1/2)3=7/8

approve if usefull
2061 Points
8 years ago
the probability will be 7/8
you can solve it using the tree diagram and then amking the cases
733 Points
8 years ago

According to me there are 4 possible outcomes.

BGG  BBGbbg,bgg,bbb,ggg

Out of these four outcomes, 33 are favorable. So the probability should be ¾.