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Question 5 Cystic fibrosis (CF) is a recessive gene disease meaning that a child has to...

Question 5

Cystic fibrosis (CF) is a recessive gene disease meaning that a child has to inherit a defective CF gene from each parent. This means that there is a 25% chance of a child having cystic fibrosis if both parents are CF carriers Hence the number of children with CF (in a family whose parents are CF carriers) has a binomial distribution with n = the number of children in the family and p= 0.25

i. In a family of four (4) children whose parents are CF carriers, what is the probability that exactly one (1) of the children has cystic fibrosis. (2 mark)

ii. In a family of six (6) children whose parents are CF carriers, what is the probability that one or more of the children has cystic fibrosis.

Math   Statistics-And-Probability   
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Answer #1

i)

Sample size , n =    4
Probability of an event of interest, p =   0.25


P ( X = 1) = C (4,1) * 0.25^1 * ( 1 - 0.25)^3=      0.4219

...........

ii)

Sample size , n =    6
Probability of an event of interest, p =   0.25

X P(X)
0 0.1780
1 0.3560
2 0.2966
3 0.1318
4 0.0330
5 0.0044
6 0.0002

p(x>=1) = 1-p(0)

=1-0.178

=0.8220

................

THANKS

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