A bag holds 5 red beads and 3 blue beads. One bead is drawn and its colour noted, then it is put back before a second bead is drawn. What is the probability of red first and blue second?
A15 out of 56
B15 out of 64
C8 out of 64
D1 out of 2
Answer & Solution
Correct answer: B. 15 out of 64
1. The bead is replaced, so the bag is identical for both draws and the two events are independent.
2. There are 5 plus 3 beads in the bag, which is 8 beads in total.
3. The probability that the first bead is red is 5 out of 8.
4. Because the bead goes back, the bag still holds 8 beads for the second draw.
5. The probability that the second bead is blue is therefore 3 out of 8.
6. For independent events the two probabilities are multiplied together.
7. Five multiplied by 3 is 15 and 8 multiplied by 8 is 64, so the answer is 15 out of 64.
8. The answer 15 out of 56 is the trap for forgetting the replacement and using 7 beads on the second draw, 8 out of 64 adds the probabilities instead of multiplying, and 1 out of 2 ignores the counts entirely.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 10: Probability_
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