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June 2018 p61 q6
3016
Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of the vehicles approaching this particular junction from town A, 55% turn left, 15% turn right and 30% go straight on. The direction a vehicle takes at the junction is independent of the direction any other vehicle takes at the junction.
Find the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right.
Solution
Let S be the event that a vehicle goes straight, L be the event that a vehicle turns left, and R be the event that a vehicle turns right.
The probability that one vehicle goes straight and the other two turn left is given by:
\(P(SLL) = (0.3)(0.55)(0.55) = 0.09075\)
The probability that one vehicle goes straight and the other two turn right is given by:
\(P(SRR) = (0.3)(0.15)(0.15) = 0.00675\)
There are 3 ways to arrange SLL (SSL, SLL, LSL) and 3 ways to arrange SRR (SSR, SRR, RSR), so the total probability is: