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Probability — MATHS STD 7 — Question

ICSE BoardEnglish MediumSTD 7MATHSProbability5 Marks
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’)
✓

Answer

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 $\mathrm{E}$........ $[\because P(E)=36 \%$ maximun $]$
(ii) The least chances of winning the race is of Student $C$......... $[\because P(C)=7 \%$ minimum $]$
(iii) The sum of the probabilities
$ \begin{aligned} & =P(A)+P(B)+P(C)+P(D)+P(E) \\ & =20 \%+22 \%+7 \%+15 \%+36 \% \\ & =100 \% \end{aligned} $
(iv) Favourable outcomes that either A or D will win $=20 \%+15 \%=35 \%$
$P\left(\right.$ either $A$ or $D$ will win) $=\frac{35}{100}=\frac{7}{20}$
(v) (a) Favourable outcomes that B will win $=22 \%$
$ P(S)=\frac{22}{100}=\frac{11}{50} $
(b) $\mathrm{S}^{\prime}=\mathrm{B}$ will not win the race.
(c) $P\left(S^{\prime}\right)=1-P(S)$
$ =1-\frac{11}{50}=\frac{50-11}{50}=\frac{39}{50} $

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