If there were fifteen cards left in the deck, and five were diamonds, what is the probability that two cards dealt (without replacement) would both be diamonds?
5/15 * 4/14
How did you get that answer?
there were 15 cards, 5 of them diamonds. So, the chance of getting a diamond is 5/15
After that, having drawn a diamond, there are only 14 cards left, 4 of them diamonds. So, the chance that the 2nd draw is another diamond is 4/14.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To calculate the probability of drawing two cards that are both diamonds, we need to use the concept of conditional probability.
First, let's find the probability of drawing a diamond on the first card. Since there are initially 15 cards left in the deck, out of which 5 are diamonds, the probability of drawing a diamond on the first card is 5/15.
After drawing the first diamond, there are now 14 cards left in the deck, with 4 diamonds remaining. Therefore, the probability of drawing a second diamond, without replacement, is 4/14.
To find the probability of both events (drawing two diamonds) happening, we need to multiply the probabilities of the individual events. So, the probability of drawing two diamonds is (5/15) * (4/14).
Let's simplify this expression:
(5/15) * (4/14) = (1/3) * (2/7) = 2/21.
Therefore, the probability of drawing two cards that are both diamonds is 2/21.