The problem of statistics is given in two sections of same standard. The odds against for section x to slove the problem are 4 ∶ 3 and odds in favour to section Y for solving the same problems are 7 ∶ 8. The probability that neither section solves the problem of statistics, if both sections try independent of each other, is:
Step 1 — Convert odds to probabilities:
Odds against X solving = 4 : 3, so \(P(\bar{X}) = \dfrac{4}{7}\).
Odds in favour of Y solving = 7 : 8, so \(P(Y) = \dfrac{7}{15}\) and \(P(\bar{Y}) = \dfrac{8}{15}\).
Step 2 — Apply independence:
\[P(\text{neither solves}) = P(\bar{X})\cdot P(\bar{Y}) = \dfrac{4}{7}\times\dfrac{8}{15} = \dfrac{32}{105}\]
Therefore the required probability is \(\dfrac{32}{105}\).
Important Questions from Odds of an Event
If n > 7, then what is the probability that C(n, 7) is a multiple of 7?
Three candidates solve a question. Odds in favour of the correct answer are 5 : 2, 4 : 3 and 3 : 4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly?
A Mathematics problem is given to two students X and Y to solve. The odds in favour of X solving the problem are 6 to 9 and the odds against Y in solving the problem are 6 to 5. What is the probability that the problem will be solved if both X and Y try to solve the problem?
