Handling Data 5
3 marks · EasyA number card is chosen at random from a box containing 6 cards numbered 1 to 6. The card is replaced and another card is chosen.
Find the probability that both cards show an even number.
What is the probability that one card shows an odd number and one card shows an even number?
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(a) \frac{1}{9}
(b) \frac{4}{9}
Common mistakes: Not multiplying probabilities; For (b), forgetting to consider both possible orders
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Marking points
M1 (a) · 1 mark · For multiplying probabilities for two even numbers
M2 (b) · 1 mark · For recognising both possibilities (odd then even, even then odd)
A1 (b) · 1 mark · For a correct answer for (b) ()
Worked solution
There are 3 even (2,4,6) and 3 odd (1,3,5) on each pick.
(a) Both even:
(b) One odd, one even: two ways (odd then even, even then odd)