Calculating Probability & Expected Wins in Betting Game

[xChee]

In a betting game a player gets to 3 chances to play after betting 6 dollars. The player must roll a 4 on a die. If he doesn't he loses. If he does then he can advance to the next round where he can then draw 3 cards from a deck of 8 consisting of 2 kings, two queens, two jacks and 2 jokers. If he draws the 2 jokers then he wins the game (does't matter what the third card is). The prize for winning the game is 30 dollars plus the 6 he originally used to play the game. So in total 36 dollars.

a) what's the probability of rolling a 4?

is it 1/6?

b) what's the probability of drawing 2 jokers?

is it (2C2)(6C1)/(8C2)

which is, 6/28

c) what is the probability of winning?

is it
(1/6)(6/28)
which is 1/28 ?

d) What is the expected value of one bet?

is it

E(x)= ( ∑ xi)(P(x))=((-6.00)(27/28))((30.00)(1/28))
= -1215/196 dollars?

e) Calculate his expected number of wins in those 3 trails

is it (3)(1/28) ?

 

[haruspex]

Is it (2C2)(6C1)/(8C2)

(2C2)(6C1)/(8C3) = 3/28

d) What is the expected value of one bet?

is it

E(x)= ( ∑ xi)(P(x))=((-6.00)(27/28))((30.00)(1/28))
= -1215/196 dollars?

You have turned a sum into a product.
E(x)= ∑ x_i P(x_i)