ITPEC FE Morning October 2022 Question 6
There are three (3) blue balls and four (4) green balls in a box. When two balls are randomly taken out from the box, what is the probability that both are blue?
Explanation
1/7 — the balls are drawn without replacement, so the second draw has one blue ball and one ball fewer.
- •First ball blue: 3 ÷ 7
- •Second ball blue, given the first was: 2 ÷ 6
- •Both blue: 3 ÷ 7 × 2 ÷ 6 = 6 ÷ 42 = 1 ÷ 7
Counting pairs gives the same: 3 of the 21 possible pairs of balls are both blue, 3 ÷ 21 = 1 ÷ 7.
Answer (c)
Why not others:
- •(d) 9/49 — (3 ÷ 7)2, which assumes the first ball is put back before the second draw
- •(a) 2/49 and (b) 1/15 — match neither way of drawing: without replacement it is 3 blue pairs out of 21, and even with replacement it is 9/49
Key rule: Without replacement, reduce both the count of the wanted colour and the total after each draw, or count combinations: C(3, 2) ÷ C(7, 2).
Basic Theory · AI-written, may contain errors
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