Question

A person bets 1 dollar to b dollars that he can draw two cards from an ordinary deck of cards without replacement and that they will be of the same suit. Find b so that the bet is fair.

Answer 1

Answer:

$3.25

Step-by-step explanation:

In an ordinary deck of cards, we will notice that there are 52 cards.

However, we have 4 suits and 13 cards in each one making a total of 52, right?.

So, the probability that a person draws two cards and they will be of the same   suit is:

$P(X) =\dfrac{ \bigg (^4_1 \bigg) \times \bigg ( ^{13}_{2}\bigg) }{ \bigg ( ^{52}_{2} \bigg)}$

$P(X) =\dfrac{ \dfrac{4!}{1!(4-1)!} \times \dfrac{13!}{2!(13-2)!} }{ \dfrac{52!}{2!(52-2)!} }$

$P(X) =\dfrac{4}{17}$

Given that; A person bets 1 dollar to b dollars;

To make the bet fair is;

$\dfrac{4}{17}b - \dfrac{13}{17}(1) = 0$

$= \dfrac{4}{17}b = \dfrac{13}{17}$

multiply both sides by 17

4b = 13

b = 13/4

b = 3.25

Therefore, to make the fair, the value of b need to be $3.25