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Question
Five Students A, B, C, D, and E are competing in a long-distance race. Each student’s probability of winning the race is given below:
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
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Solution
Given probabilities of five students A, B, C, D, and E such as
P(A) = 20%, P(B) = 22%, P(C) = 7%, P(D) = 15%, and P(E) = 36%
(i) The mostly chance of winning the race is of Student E. ..........[∵ P(E) = 36% maximun]
(ii) The least chances of winning the race is of Student C. ..........[∵ P(C) = 7% minimum]
(iii) The sum of the probabilities
= P(A) + P(B) + P(C) + P(D) + P(E)
= 20% + 22% + 7% + 15% + 36%
= 100%
(iv) Favourable outcomes that either A or D will win = 20% + 15% = 35%
P(either A or D will win) =`35/100=7/20`
(v) (a) Favourable outcomes that B will win = 22%
P(S) =`22/100=11/50`
(b) S' = B will not win the race.
(c) P(S') = 1 − P(S)
= `1-11/50=(50-11)/50=39/50`
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