Handling Data 5
2 marks · HardA bag contains 5 blue counters and 3 red counters. Two counters are picked from the bag one after the other, without replacement. What is the probability that both counters picked are red?
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(±0.01)
Also accept: 3/28; 0.107; 0.11
Common mistakes: Using replacement instead of without replacement: ; Incorrect denominators or numerators
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Marking points
M1 · 1 mark · Uses correct method for dependent events: multiplies probability of first red by probability of second red after one red has been removed.
A1 · 1 mark · Correctly calculates or a correct equivalent decimal fraction (accept to 2 decimal places).
Worked solution
The probability that the first counter picked is red is . After removing one red counter, there are now 2 red counters left out of 7 total counters.
Therefore, the probability that both counters are red is or about 0.11.