Handling Data 5
4 marks · HardMaria chooses a marble from bag X and a marble from bag Y. In bag X there are 4 red and 6 blue marbles. In bag Y there are 3 red and 5 blue marbles.
She claims: 'Picking a blue marble from bag X and a red marble from bag Y is independent from picking a red marble from bag X and a blue marble from bag Y.' Is Maria correct? Give reasons for your answer.
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Yes, Maria is correct. The two events (choosing blue from X/red from Y and red from X/blue from Y) are independent because the selection from bag X does not affect the selection from bag Y; the bags are separate, so the probabilities of each outcome are multiplied.
Must show: Reference to separate bags or selections, Explanation that probability of one choice does not affect the other, Correct application of the concept of independent events
Also accept: Yes, the two choices are independent because picking from one bag does not change the possible outcomes in the other bag.
Common mistakes: Saying the events are dependent; Ignoring the independence due to separate bags
Show mark scheme and worked solution
Marking points
B1 · 1 mark · States clearly whether the events are independent.
M1 · 1 mark · Correctly identifies that the choices come from different bags.
M2 · 1 mark · Explains the definition of independent events; probability of one event does not affect the other.
A1 · 1 mark · Provides a valid reason or an example using probabilities if appropriate.
Worked solution
Yes, Maria is correct. The two events are independent because each marble is picked from a different bag. The result of picking a marble from bag X does not affect the probabilities in bag Y. For example, the probability of picking blue from X is 6/10 and the probability of picking red from Y is 3/8. The overall probability of these two outcomes together is (6/10) × (3/8), showing the events are independent.