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Standard X

Mathematics

Probability

Three student...

Question

Three students $A, B$ and $C$ are to take part in a swimming competition. The probability of $A$ 's winning or $B$ 's winning each is $3$ times the probability of $C$ 's winning. The probability of $C$ 's winning if there is no tie is:

\frac{4}{7}

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\frac{3}{7}

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\frac{2}{7}

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\frac{1}{7}

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Solution

The correct option is D $\frac{1}{7}$
Let's say chances of winning $C$ is $= x$
Then chances of winning $A$ is $= 3 x$
And chances of winning $B$ is $= 3 x$
$P (A) + P (B) + P (C) = 1$
Probability of $C$ winning is $= \frac{1}{7}$

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Three students A,B and C are to take part in a swimming competition. The probability of A's winning or B's winning each is 3 times the probability of C's winning. The probability of C's winning if there is no tie is:

The correct option is D 17Let's say chances of winning C is =xThen chances of winning A is =3x And chances of winning B is =3xP(A)+P(B)+P(C)=1Probability of C winning is =17

Three students $A, B$ and $C$ are to take part in a swimming competition. The probability of $A$ 's winning or $B$ 's winning each is $3$ times the probability of $C$ 's winning. The probability of $C$ 's winning if there is no tie is:

The correct option is D $\frac{1}{7}$
Let's say chances of winning $C$ is $= x$
Then chances of winning $A$ is $= 3 x$
And chances of winning $B$ is $= 3 x$
$P (A) + P (B) + P (C) = 1$
Probability of $C$ winning is $= \frac{1}{7}$