Homework Sourseassueme PrboyPrgirl05 Then if there are four children what i
assueme Pr(boy)=Pr(girl)=0.5. Then if there are four children what is the Probability that,
a)All four are the same gender
b)three are the same gender
C) two are boys and two are girls
d)what is the mean of the distribution
e)what is the variance of the distribution
f)what is the standard deviation
g)coefficient of variation
h)coefficient of dispersion
Solution
a)
Let x = the number of boys.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 4
p = the probability of a success = 0.5
x = the number of successes = 4
Thus, the probability is
P ( 4 ) = 0.0625
As the probability of all girls are the same, we multiply this by 2:
P(All same gender) = 0.0625*2 = 0.125 [ANSWER]
****************
B)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 4
p = the probability of a success = 0.5
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.25
As the probability of getting 3 girls are the same, we multiply this by 2:
P(3 same gender) = 0.25*2 = 0.50 [ANSWER]
********************
c)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 4
p = the probability of a success = 0.5
x = the number of successes = 2
Thus, the probability is
P ( 2 ) = 0.375 [ANSWER]
********************
d)
u = mean = np = 2
e)
sigma^2 = variance = np(1-p) = 1
f)
sigma = standard deviation = sqrt(np(1-p)) = 1
g)
COV = sigma/u = 1/2 = 0.5 [ANSWER]
h)
COD = sigma^2/u = 1^2 / 2 = 0.5 [ANSWER]
