Question

suppose that you and a friend are playing cards and you decide to make a friendly wager.the best is that you will draw two cards without replacement from a standard deck.if both cards are diamonds your friend will pay $801.otherwise you have to pay our friend $48

Answer 1

Total number of cards in a standard deck of card=52

As deck of card contain 13 club +13 heart +13 spade+13 Diamond.

P(Diamond)=13/52 =1/4

If the card is not diamond then

P(not diamond)=39/52=3/4

Since after drawing card is not replaced

P ( second Diamond)=12/51

now if second card is not Diamond.then

P(non diamond)=39/51

Chances of your winning i.e both cards are diamonds=1/4×12/51=1/17=0.0588..(approx)

chances of your friend winning=1/4×39/51=[1/4]×[13/17]=13/68=0.1911..(approx)

Your friend has got better chance to win because there are more chances that both the cards are not Diamonds.