Subtopic: Mean, median, mode and standard deviation
Question Statement:
Probability and Statistics: Mean, median, mode and standard deviation; random variables; Poisson, normal and binomial distributions; correlation and regression analysis.
In a relay race there are five teams A, B, C, D, E. Assuming each team has an equal chance of any position (1st–5th), the probability that A, B, C finish 1st, 2nd, 3rd respectively is
Options:
(A) 1/60
(B) 1/20
(C) 1/10
(D) 3/10
Official Answer Key:
A
Step-by-Step Solution & Explanation
Total equally-likely arrangements of 5 teams in 5 positions = 5! = 120. Favourable outcomes: A must occupy 1st, B must occupy 2nd, C must occupy 3rd (fixed); D and E may occupy the remaining two positions (4th, 5th) in any order, giving 2! = 2 ways. P = 2/120 = 1/60. Equivalently, sequentially: P(A first)=1/5, P(B second | A placed)=1/4, P(C third | A,B placed)=1/3 → 1/5×1/4×1/3 = 1/60. Answer: (A) 1/60.
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