Trudi Can Either Walk TO School, Or She Can Take The Bus. The Probability Of Her Taking The Bus On Any Given Day Is 0.77.
Assuming That Her Choice Of Transport On Any Given Day Is Independent Of Her Choice Of Transport On Another Day, Find Out The Probability Of Her Taking The Bus To School On Exactly 3 Days, Out Of A Total Of 5 Days.
p=P(B)=0.77
q=1-P(B)=0.23 = probability of walking
n=5 (days)
r=3 days taking bus
Given independence of choice from day to day, and probability does not vary, then we can use the binomial distribution.
To calculate the probability of taking the bus exactly r days out of n:
P(n,r,p)=nCr*p^r*(1-p)^(n-r)
For 3 days out of 5,
probability = P(5,3,0.77)
which turns out to be about a quarter.