Select 2 cards from a deck of 52,
a. Find the probability of getting 2 hearts
b. Find the probability of getting a heart on the 2nd draw given that you got a heart on the first draw
A. There are 13 hearts from a standard deck of 52 cards. Therefore, there is a 13/52, or 1/4, chance of choosing a heart. Now, there are 12 out of 51 hearts to choose from. The probability of choosing a second heart is 12/51, or 4/17. Thus, the probability of drawing 2 hearts is 1/4*4/17 = 1/17.
Without replacment
Pr(2hearts)=13/52*12/51
pr(second heart|firstcard was heart)=12/51
Refer to A. for the answer to b.
Oops, I meant 12 hearts out of 51 cards, not 51 hearts.
To find the probability of the events in both parts (a) and (b), we need to know the total number of possible outcomes as well as the number of successful outcomes for each event.
a. To find the probability of getting 2 hearts, we need to first determine the total number of possible outcomes. Since we are selecting two cards from a standard deck of 52 cards, there are 52C2 (52 choose 2) possible outcomes.
Next, we need to determine the number of successful outcomes, i.e., the number of ways we can choose 2 hearts from the deck. There are 13 hearts in a deck, so the number of ways to choose 2 hearts is 13C2 (13 choose 2).
Using the formula for probability:
Probability of getting 2 hearts = Number of successful outcomes / Total number of possible outcomes
Therefore, the probability of getting 2 hearts is:
(13C2) / (52C2)
b. To find the probability of getting a heart on the 2nd draw given that you got a heart on the first draw, we need to calculate the conditional probability.
First, let's consider the successful outcome, which is getting a heart on the second draw given that you already got a heart on the first draw. Since we are selecting cards without replacement, after you already picked a heart on the first draw, there are only 51 cards left in the deck, with 12 of them being hearts.
Therefore, the number of successful outcomes for this event is 12 (the 12 remaining hearts).
Next, we need to consider the total number of possible outcomes, which is the same as the previous event (52C2) since we are still selecting two cards from the original deck of 52 cards.
Using the formula for conditional probability:
Probability of getting a heart on the 2nd draw given that you got a heart on the first draw = Number of successful outcomes / Total number of possible outcomes
Therefore, the probability of getting a heart on the 2nd draw given that you got a heart on the first draw is:
12 / (52C2)