The probability of an event lies between 0 and 1, inclusive. This means: \[ 0 \leq P(\text{Event}) \leq 1 \] Option (A) 0 is a valid probability, representing an impossible event.
Option (B) 1 is a valid probability, representing a certain event.
Option (D) 0.99999 is a valid probability, as it is still within the range [0, 1].
However, option (C) 1.0001 is not a valid probability because it exceeds the upper limit of 1.
The correct option is (C): \(1·0001\)
If \(S=\{1,2,....,50\}\), two numbers \(\alpha\) and \(\beta\) are selected at random find the probability that product is divisible by 3 :
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: \( P(3 < x \leq 6) \)