Need help on how to solve this problem..
Five cards are chosen from a deck of playing cards and put into a pile. Three of the cards are red and 2 of the cards are black. A second pile is made using 2 red cards and b black cards. One card from each pile is chosen randomly. The probability of choosing a red card from each of the piles is 6/45. How many black cards, b , are in the second pile? The answer is 7 but I don't know why that is the answer. Thanks...
call the 2 piles x and y
P(x) = 3/5
P(y) = 2/(b+2)
3/5 * 2/(b+2) = 6/45
6 / 5(b+2) = 6/45
5(b+2) = 45
b+2 = 9
b = 7
To solve this problem, we can use the concept of probability. Let's break down the given information:
We have two piles:
- The first pile consists of 5 cards, with 3 of them being red and 2 being black.
- The second pile consists of 2 red cards and "b" black cards (the value we are trying to find).
We are asked to calculate the probability of choosing a red card from each pile, which is given as 6/45.
To find out the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
For the first pile, the favorable outcome is choosing a red card, and there are 3 red cards in the pile. The total number of possible outcomes is 5 because there are 5 cards in total.
Therefore, the probability of choosing a red card from the first pile is 3/5.
Now, let's move on to the second pile. The favorable outcome is again choosing a red card, and the number of red cards is 2. The total number of possible outcomes is b + 2 (since there are "b" black cards and 2 red cards).
Therefore, the probability of choosing a red card from the second pile is 2/(b + 2).
As per the given information, the probability of choosing a red card from each pile is 6/45. So, we can set up an equation:
(3/5) * (2/(b + 2)) = 6/45
To simplify the equation, we can multiply both sides by 45 to eliminate the fractions:
9 * 2 = 3 * (b + 2)
18 = 3b + 6
3b = 12
b = 4
Therefore, the second pile has 4 black cards (b = 4), not 7 as you mentioned. It seems that there might be a mistake in the final answer you provided.