Handling Data 5
4 marks · HardA box contains 3 orange balls and 2 purple balls. A ball is picked at random, not replaced, then a second ball is picked at random.
Calculate the probability that: (a) Both balls are orange (b) The two balls picked are different colours
Calculate the probability that both balls are orange.
Calculate the probability that the two balls are different colours.
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) 3/10
(b) 6/10 or 3/5
Common mistakes: Incorrectly using replacement (independent events); Errors in fractions or numerators/denominators
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Multiplies correct probabilities for first and second orange ball (3/5 × 2/4 or equivalent).
A1 (a) · 1 mark · Gives final answer 3/10 for both orange.
M2 (b) · 1 mark · Adds probabilities for orange then purple, and purple then orange, or finds 1 minus probability of both same. (follow-through)
A2 (b) · 1 mark · Gives final answer 6/10 or 3/5 for different colours. (follow-through)
Worked solution
(a) Probability of first ball orange: 3/5. Probability of second ball orange (after one orange removed): 2/4 = 1/2.
So, probability both orange = 3/10.
(b) Probability of first orange then second purple: (3/5) × (2/4) = 3/10 Probability of first purple then second orange: (2/5) × (3/4) = 6/20 = 3/10 Total probability = 3/10 + 3/10 = 6/10 = 3/5