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9709 statistics

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.
Reply 2
For SLL you could have
SLL
LSL
LLS
all have the same probability, so you multiply it by 3 or 3C1 to account for all 3 different events occurring.
Original post by thenerdygeek
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.
Oh that does make sense. Thank you so much!
i am sitting for the exam today just the same. i came across this ques but what i dont understand is this: we have three different vehicles so why dont we multiply it by 3! ? why do we multiply it with 3 only?

Original post by mqb2766
For SLL you could have
SLL
LSL
LLS
all have the same probability, so you multiply it by 3 or 3C1 to account for all 3 different events occurring.
Reply 5
There are only 3 combinations, not 3!
Original post by Aleema Imran
i am sitting for the exam today just the same. i came across this ques but what i dont understand is this: we have three different vehicles so why dont we multiply it by 3! ? why do we multiply it with 3 only?
Reply 6
Stats>>>>Pure
Reply 7
how was the stats paper and what were the answers ?
thanks for the answer. the exam went great thank God.
Original post by mqb2766
There are only 3 combinations, not 3!
is CIE okay with posting answers? its a bit pedantic but i am unsure

Original post by Aleema Imran
thanks for the answer. the exam went great thank God.


Original post by Unkonwn
how was the stats paper and what were the answers ?
The complex numbers u and v are given by u = 1 + 2ï3i and v = 3 + 2i. In an Argand diagram,
u and v are represented by the points A and B. A third point C lies in the first quadrant and is
such that BC = 2AB and angle ABC = 90Å. Find the complex number z represented by C, giving
your answer in the form x + iy, where x and y are real and exact
Reply 11
P(SLL)P(SRR)P(LSL)P(LLS)P(RSR)P(RRS)add them, you'll get the answer

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