Example 1
A bag has 2 red and 4 blue counters. Two are drawn without replacement. What is the probability of one of each colour, in either order?
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Answer: 158
- Add red–blue and blue–red.
- 6×52×4+4×2=158.
Example 2
A bag has 4 red and 2 blue counters. Two counters are drawn without replacement. Given that at least one is red, what is the probability that both are red?
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Answer: 73
- Restrict to outcomes with at least one red: 30−2=28 ordered outcomes.
- 12 have two reds, giving 73.
Example 3
A selector has 3 equal sectors labelled A and 3 equal sectors labelled B. It picks a bag, then a counter is drawn uniformly from that bag. Bag A has 1 red out of 7 counters; Bag B has 5 red out of 9. Given that the counter is red, what is the probability Bag A was selected?
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Answer: 449
- Joint red probabilities are (63)×(71) and (63)×(95).
- Restrict to red outcomes: A’s share is 27+10527=449.