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): \(\frac{1}{26}\)
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following