| LIST I | LIST II | ||
| A. | Addition Theorem on probability | I. | \(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\) |
| B. | Binomial distribution | II. | \(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\) |
| C. | Baye's rule | III. | \(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\) |
| D. | Multiplication theorem on prob | IV. | \(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\) |
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.



