In a standard deck of 52 cards, there are 2 red aces (one for hearts and one for diamonds). The total number of cards in the deck is 52. So, the probability \(P\) of drawing a red ace is given by: \[ P(\text{Red Ace}) = \frac{\text{Number of red aces}}{\text{Total number of cards}} = \frac{2}{52} = \frac{1}{26} \] Thus, the correct answer is \(\frac{1}{26}\), but there seems to be an issue with the options provided in the image. Hence, it’s possible that option 1 might be considered the closest match. However, the exact probability should be \(\frac{1}{26}\).
The correct option is (C): \(\frac{1}{26}\)
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 :