Question

1. Two cards are drawn randomly from a standard deck of 52 playing cards. You win $20 if these two cards contain any one pair. What is the probability that you will win this $20?

2. Referring to the previous problem, you can also win $5 if the two cards you drew contain one or more hearts. Whats the probability that you will win anything, including the $20 described above?

Answer 1

I know the answer to the first part. It's 0.059, however the second question is confusing depending on how you read it

Answer 2

how can you find first quetion's answer? can you tell me a bit

Answer 3

1. There are 52 choices for the first card, and there are 51 choices for the second card. Therefore the total number of combinations of the two cards is: 52 * 51.
Having drawn the first card, there are three choices for the second card (one choice from each of the remaining suits) to make a pair. Therefore the number of combinations to make a pair is: 52 * 3.
The probability of drawing a pair is given by:
\[P(pair)=\frac{52\times3}{52\times51}=0.0588\]

Answer 4

Any ideas for the second one?

Answer 5

2. The probability of getting one heart and no pair from the other three suits is:
\[\large P(1\ heart,\ no\ pair)=\frac{13\times37}{52\times51}=0.181\]
The probability of getting two hearts is:
\[\large P(2\ hearts)=\frac{13\times12}{52\times51}=0.059\]
These two events and the event 'get any one pair' are mutually exclusive. Therefore the probability that you will win anything, including the $20 is found by adding the three values of probability.