Step 1: Understand equally likely outcomes
Equally likely outcomes refer to situations where each possible outcome has the same probability of occurring.
Step 2: Analyze each option
Option (1): Tossing a coin has two equally likely outcomes: heads and tails.
Option (2): Tossing two coins simultaneously has four equally likely outcomes: (HH, HT, TH, TT).
Option (3): Rolling two dice also has 36 equally likely outcomes, as each die has 6 faces, giving 6 × 6 = 36 possibilities.
Step 3: Conclusion
All of the options represent situations with equally likely outcomes. Hence, the correct option is \( (4) \).
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 :