Handling Data 4
4 marks · NormalA bag contains 5 red balls and 3 blue balls. Two balls are taken out one after the other, without replacement.
Draw a tree diagram to represent all possible outcomes.
Calculate the probability that both balls are the same colour.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) — · must show Branches for first ball: R(5/8), B(3/8); second ball probabilities update depending on first pick
(b) 20/56 + 6/56 = 26/56 = 13/28 = 0.46 (rounded)
Must show: Branches must show probabilities for both draws, Correct labels (R, B, combinations)
Common mistakes: Assuming replacement; Using wrong denominators on second draw
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Draws correct branches for first pick: R (5/8), B (3/8).
A1 (a) · 1 mark · Second branches show updated probabilities: after R (4/7), after B (2/7).
M2 (b) · 1 mark · Proper multiplication of probabilities for same-colour cases.
A2 (b) · 1 mark · Adds both probabilities: (5/8 × 4/7) + (3/8 × 2/7) = 20/56 + 6/56 = 26/56 = 13/28 = 0.46.
Worked solution
a) First pick: 5/8 red, 3/8 blue.
If red first, next is 4/7 red or 3/7 blue. If blue first: 5/7 red or 2/7 blue.
Both red: 5/8 × 4/7 = 20/56. Both blue: 3/8 × 2/7 = 6/56.