# Five Students A, B, C, D and E are competing in a long distance race.

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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’)

by (-3,448 points)

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% maximum]

(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