Correct answer: \(\frac{3}{5}\)
Explanation:
The total number of balls in the bag is: \[ 4 \, \text{(black balls)} + 6 \, \text{(red balls)} = 10 \, \text{balls} \] The number of red balls is 6. Therefore, the probability of drawing a red ball is: \[ P(\text{red ball}) = \frac{\text{number of red balls}}{\text{total number of balls}} = \frac{6}{10} = \frac{3}{5} \]
Hence, the probability of drawing a red ball is \(\frac{3}{5}\).
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: \( P(3 < x \leq 6) \)