ITPEC IP October 2023 Question 1
ITPEC IP October 2023 — Question 1 of 100
Drawing three black balls in order has the lowest probability. Because balls are not returned, multiply the changing conditional probabilities for each sequence.
- •BBB:
4/7 × 3/6 × 2/5 = 24/210 - •BBW:
4/7 × 3/6 × 3/5 = 36/210 - •BWB:
4/7 × 3/6 × 3/5 = 36/210 - •WBB:
3/7 × 4/6 × 3/5 = 36/210
The first black draw is relatively likely, but after two black balls have been removed only two black balls remain, making the third black draw less likely than the corresponding white draw.
Answer (a)
Key rule: For draws without replacement, update the numerator and total after every draw, then multiply the conditional probabilities.
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