In a race, the odd favour of cars P, Q, R, S are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find the probability that one of them wins the race.
A. $$\frac{{9}}{{17}}$$
B. $$\frac{{114}}{{121}}$$
C. $$\frac{{319}}{{420}}$$
D. $$\frac{{27}}{{111}}$$
Answer: Option C
Solution(By Examveda Team)
Let the probability of winning the race is denoted by P(person)$$\eqalign{ & P(P) = \frac{1}{4}, \cr & P(Q) = \frac{1}{5}, \cr & P(R) = \frac{1}{6}, \cr & P(S) = \frac{1}{7} \cr} $$
All the events are mutually exclusive (since if one of them wins then other would lose as pointed out by rahul) hence,
Required probability:
$$ = P(P) + P(Q) + P(R)$$ $$ + P(S)$$
$$\eqalign{ & = \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} \cr & = \frac{{319}}{{420}} \cr} $$
Related Questions on Probability
A. $$\frac{{1}}{{2}}$$
B. $$\frac{{2}}{{5}}$$
C. $$\frac{{8}}{{15}}$$
D. $$\frac{{9}}{{20}}$$
A. $$\frac{{10}}{{21}}$$
B. $$\frac{{11}}{{21}}$$
C. $$\frac{{2}}{{7}}$$
D. $$\frac{{5}}{{7}}$$
A. $$\frac{{1}}{{3}}$$
B. $$\frac{{3}}{{4}}$$
C. $$\frac{{7}}{{19}}$$
D. $$\frac{{8}}{{21}}$$
E. $$\frac{{9}}{{21}}$$
What is the probability of getting a sum 9 from two throws of a dice?
A. $$\frac{{1}}{{6}}$$
B. $$\frac{{1}}{{8}}$$
C. $$\frac{{1}}{{9}}$$
D. $$\frac{{1}}{{12}}$$
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