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**Probability 2: constructing tree diagrams**

IB Studies Adrian Sparrow

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AND and OR 1 A bag contains 3 red counters and 2 blue counters. A counter is picked at random, then replaced in the bag. A counter is then chosen again. b) Find the probability that 2 blue counters are picked. a) Find the probability that 2 red counters are picked. c) Find the probability that the 2 counters are picked are the same colour.

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AND and OR 2 A tired maths teacher reaches into her sock draw in the morning. She has 5 black and 3 red socks in the draw. She picks two socks at random. Find the probability that she picks, b) two red socks, a) two black socks, c) matching socks, Note that this is a question without replacement, so be careful with the second probability. d) socks of different colours.

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**Tree diagrams - construction**

A bag contains 3 red counters and 2 blue counters. A counter is picked at random, then replaced in the bag. A counter is then chosen again. Show this information on a tree diagram. 1st choice 2nd choice red red blue red blue blue

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**Tree diagrams - reading a table**

Always fill in the probabilities on at the end of the branches, keep the denominators the same and ensure the total is 1. This makes answering questions much easier. Find the probability that c) the 2 counters picked are of the same colour, a) 2 red counters are picked, d) the 2 counters are picked are of different colours. b) blue counters are picked,

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**Question Male Female SL SL HL SL HL HL**

An IB group has 10 males and 10 females. 4 males do SL maths and 6 do HL maths. 7 females do SL and 3 do HL maths. One male and one female are chosen at random and their level of maths is noted. a) Construct a tree diagram for this data. Hence, calculate the probability that when a male and female are chosen at random, Male Female SL SL b) both do HL, HL c) both do SL, SL HL d) one does HL, and one does SL. HL e) the male does HL, the female does SL.

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