Correct answer: 8
Explanation:
When a coin is tossed, it has 2 possible outcomes: Heads (H) or Tails (T). For three coins, each coin can independently show either Heads or Tails. Therefore, the total number of outcomes for three coins is: \[ 2 \times 2 \times 2 = 8 \] The possible outcomes are: \[ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \]
Hence, the total number of outcomes is 8.
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: \( P(3 < x \leq 6) \)