Question

We select 5 cards without replacement from a

standard 52 card deck. Given I have two hearts in my hand, what is
the probability I'll have exactly three hearts in
my hand?

Answer 1

0.008

Explanation:

Well in a 52 card deck we have 4 signs. So the number of cards for each sign should be equal so 52÷4 = 13. There are 13 hearts in a card deck.

Now you already have two in your hand so the number of heart lefts is now 11.

(also note that 2 cards are in your hand so the new total of cards left is 52 - 2 = 50)

Number of heart cards left = 11

Number of cards in total left = 50

We can use this information to find the probability that we'll have 3 more hearts in our hand.

`Probability = (11)/(50) * (10)/(49) * (9)/(48) = (990)/(117600) = 0.00841836 = 0.008`

If you're confused on what I did there, each time you take a card, the total and the number of hearts decreases by 1 (both the numerator and denominator decreases by 1) so that's why the probability is like that.