Hey! I’m doing 9709 cie a level maths (sitting for stats on may 15) and heres a statistics question i stumbled upon. Note: this is extracted from May/june 2018 paper 61.
The question goes-
‘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.
(i) 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.’
It seems like a rather simple question. I would say that we would have to find the probabilities for S,L,L and S,R,R and then add them. I found P(SLL) by 0.3 x 0.5 x 0.5 and P(SRR) using the same method. However, the markscheme doesn’t simply add the probabilities, it multiplies each one by 3C1 first then says to add them. I do not get why we need to multiply them by 3C1.
Your help would be very much appreciated!
You can find attached below the question along with the markscheme if you want to have a better look.