To the right are the outcomes that are possible when a couple has three children

Question

To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.

isis

11

girlgirl.

areare

33

boysboys.

areare

22

girlsgirls.

1st

2nd

3rd

boy

minus

boy

minus

boy

boy

minus

boy

minus

girl

boy

minus

girl

minus

boy

boy

minus

girl

minus

girl

girl

minus

boy

minus

boy

girl

minus

boy

minus

girl

girl

minus

girl

minus

boy

girl

minus

girl

minus

girl

a. What is the probability of exactly

11

girlgirl

out of three children?

nothing

(Type an integer or a simplified fraction.)

To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.

a. Among three children, there

isis

exactly

11

girlgirl.

b. Among three children, there

areare

exactly

33

boysboys.

c. Among three children, there

areare

exactly

22

girlsgirls.

1st

2nd

3rd

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boy

minus

boy

minus

boy

boy

minus

boy

minus

girl

boy

minus

girl

minus

boy

boy

minus

girl

minus

girl

girl

minus

boy

minus

boy

girl

minus

boy

minus

girl

girl

minus

girl

minus

boy

girl

minus

girl

minus

girl

Explanation / Answer

Direct MMETHOD:
a.
no. of ways = (B,G,B) (G,B,B) (B,B,G) = 3
total possiblities = 8
P(Among three children, there is exactly 1 Girl) = 3/8 = 0.375

b.
no. of ways = (B,B,B) = 1
total possiblities = 8
P(Among three children, there is exactly 1 Girl) = 1/8 = 0.125

c.
no. of ways = (B,G,G) (G,G,B) (G,B,G) = 3
total possiblities = 8
P(Among three children, there is exactly 1 Girl) = 3/8 = 0.375

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 3 * 0.5
= 1.5
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 3 * 0.5 * 0.5
= 0.75
III.
standard deviation = sqrt( variance ) = sqrt(0.75)
=0.866
a.
P( X = 1 ) = ( 3 1 ) * ( 0.5^1) * ( 1 - 0.5 )^2
= 0.375
b.
P( X = 3 ) = ( 3 3 ) * ( 0.5^3) * ( 1 - 0.5 )^0
= 0.125
c.
P( X = 2 ) = ( 3 2 ) * ( 0.5^2) * ( 1 - 0.5 )^1
= 0.375

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