Determine the probability of the events, two cards are randomly drawn from a standard deck. What is the probability of drawing a black card followed by a red card the first card is it replaced before the second card is drawn.
To determine the probability of drawing a black card followed by a red card when the first card is replaced before the second card is drawn, we can break it down into two separate events.
Event 1: Drawing a black card on the first draw
There are 26 black cards in a standard deck of 52 cards, so the probability of drawing a black card on the first draw is 26/52 = 1/2.
Event 2: Drawing a red card on the second draw
Since the first card is replaced before the second draw, there are still 26 red cards and 52 total cards in the deck. So, the probability of drawing a red card on the second draw is also 26/52 = 1/2.
Now, to find the probability of both events happening one after the other, we multiply the probabilities of each event:
P(Event 1 and Event 2) = P(Event 1) * P(Event 2) = (1/2) * (1/2) = 1/4
Therefore, the probability of drawing a black card followed by a red card when the first card is replaced before the second card is drawn is 1/4 or 25%.