Question

Tour players Harry, Ron, Harmione and Ginny are playing a card game. A deck of 52 cards are dealt out equally. If Harmione and Ginny have a total of 8 spades among them, what is the probability that Harry has 3 of the remaining 5 spades?

Answer 1

Answer: 0.339

Explanation:

Given : Tour players Harry, Ron, Harmione and Ginny are playing a card game.

. A deck of 52 cards are dealt out equally.

Then, the number of card each person has =
`(52)/(4)=13`

If Harmione and Ginny have a total of 8 spades among them, then the total cards the total spades left = 13-8=5

Now, the number of ways to get 3 of 5 spades :
`^5C_3=(5!)/(3!2!)=10`

Number of ways to draw remaining 10 cards :
`^(21)C_(10)=(21!)/(10!11!)=352716`

Also, the total cards Harmione and Ginny have = 13+13=26

Then the total cards left = 26

The number of ways to get 13 cards for Harry :

`^(26)C_(13)=(26!)/(13!(26-13)!)\\\\=(26!)/(13!13!)=10400600`

Now, the probability that Harry has 3 of the remaining 5 spades :_

`(^5C_3* ^(21)C_(10))/(^(26)C_(13))\\\\=(10*352716)/(10400600)\\\\=0.339130434783\approx0.339`

Hence, the probability that Harry has 3 of the remaining 5 spades= 0.339 (approx)