Question

an athlete is running in 4 races and in each race she has a 60% chance of winning what is the probability that she will win at least two races ?

Answer 1

probability of winning a race is 60/100=3/5
probability of loosing the race is (1-3/5)=2/5
winning atleast 2 races that means winning 2, 3 or all 4 races...
P(winning 2 races)=(3/5)x(3/5)x(2/5)x(2/5) = 36/625
P(winning 3 races)=(3/5)x(3/5)x(3/5)x(2/5) = 54/625
P(winning all 4 races)=(3/5)^4=81/625
now
P(winning atleast 2)= (36/625)+(54/625)+(81/625)=171/625

hope this helps:p