| 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. | \(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\) |
If the probability distribution is given by:
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| P(x) | 0 | k | 2k | 2k | 3k | k² | 2k² | 7k² + k |
Then find: \( P(3 < x \leq 6) \)
If \(S=\{1,2,....,50\}\), two numbers \(\alpha\) and \(\beta\) are selected at random find the probability that product is divisible by 3 :