find each probability if you pick a card, do not replace it, then pick a second 3 white cards 5 black cards and you pick black, then white
To solve this problem, we need to find the probability of drawing a black card on the first draw, and then drawing a white card on the second draw.
Step 1: Calculate the probability of drawing a black card on the first draw.
- There are a total of 8 cards (3 white and 5 black) in the deck.
- The probability of drawing a black card on the first draw is given by the number of black cards divided by the total number of cards: P(black) = 5/8.
Step 2: Calculate the probability of drawing a white card on the second draw (without replacement).
- After the first draw, there will be one less card in the deck, and the number of white cards will decrease by 1.
- There are now 7 cards remaining in the deck (2 white and 5 black).
- The probability of drawing a white card on the second draw is given by the number of white cards divided by the total number of remaining cards: P(white) = 2/7.
Step 3: Calculate the joint probability.
- The joint probability of drawing a black card on the first draw and then a white card on the second draw is equal to the product of the individual probabilities: P(black and white) = P(black) * P(white) = (5/8) * (2/7).
- Simplifying this expression, we have P(black and white) = 10/56, which can be further simplified to 5/28.
Therefore, the probability of picking a black card first, and then a white card (without replacement) is 5/28.