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June 2009 p6 q3
3050
On a certain road 20% of the vehicles are trucks, 16% are buses and the remainder are cars.
A random sample of 11 vehicles is taken. Find the probability that fewer than 3 are buses.
Solution
Let the random variable \(X\) represent the number of buses in the sample of 11 vehicles. Since 16% of the vehicles are buses, the probability of selecting a bus is \(p = 0.16\).
We need to find \(P(X < 3) = P(0) + P(1) + P(2)\).
Using the binomial probability formula \(P(X = r) = \binom{n}{r} p^r (1-p)^{n-r}\), where \(n = 11\) and \(p = 0.16\):