In a box, there are 13 white chips, 7 blue chips, and 6 green chips. Two chips…
2023
In a box, there are 13 white chips, 7 blue chips, and 6 green chips. Two chips are drawn in succession from the box. What is the probability that the two chips drawn contain one white chip and one blue chip?
- A.
50/7
- B.
25/50
- C.
7/50
- D.
None of these
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: When two items are drawn without replacement from a group containing several distinct types, the probability of drawing one item of type A and one item of type B is found as:
P = [C(nA, 1) × C(nB, 1)] / C(N, 2)
where N is the total number of items, nA and nB are the counts of the two desired types, and C(N, 2) counts every possible unordered pair from the whole group.
Application:
Total chips in the box: 13 white + 7 blue + 6 green = 26 chips, so N = 26.
Total ways to choose any 2 chips from the 26: C(26, 2) = (26 × 25) / 2 = 325.
Favorable ways — one white and one blue chip: C(13, 1) × C(7, 1) = 13 × 7 = 91.
Probability = favorable / total = 91 / 325.
Simplify by the common factor 13: 91 / 325 = 7 / 25.
Cross-check: Treat the two draws as an ordered sequence instead. P(white first, then blue) + P(blue first, then white) = (13/26)(7/25) + (7/26)(13/25) = 91/650 + 91/650 = 182/650 = 7/25 — the same result, confirming the combination approach above.
7/25 does not equal 50/7, 25/50, or 7/50, so the correct answer is ‘None of these’.