Aptitude Discussion

Q. |
There are three events $A, B$ and $C$, one of which must and only can happen. If the odds are $8:3$ against $A, 5:2$ against $B$, the odds against $C$ must be: |

✖ A. |
$13:7$ |

✖ B. |
$3:2$ |

✔ C. |
$43:34$ |

✖ D. |
$43:77$ |

**Solution:**

Option(**C**) is correct

According to the question,

\(\dfrac{P(A')}{P(A)}=\dfrac{8}{3},\;P(A)=\dfrac{3}{11}\text{ and }P(A')=\dfrac{8}{11}\)

Also \(\dfrac{P(B')}{P(B)}=\dfrac{5}{2}\)

\(P(B)=\dfrac{2}{7}\text{ and }P(B')=\dfrac{5}{7}\)

Now, out of A,B and C, one and only one can happen.

$P(A)+P(B)+P(C)=1$

\(P(C)=\dfrac{34}{77}\)

\(P(C')=1-P(C)\)

\(=\dfrac{43}{77}\)

So odd against $C$

\(\dfrac{P(C)}{P(C')}=\dfrac{43}{34}\)