You roll a die. if an odd number comes up, you lose. if you get a 6, you win $60. if it is aneven number other than 6, you get to roll again. if you get a 6 the second time, you win$36. if not, you lose.
(a) construct a probability model for the amount you win at this game. explain briefly how you obtain the probabilities associated with the different amounts of winning.
(b) how much would you be willing to pay to play this game?

Step-by-step explanation:

Given that if an odd number comes up, you lose.

i.e.

If you get 2 or 4 you roll again

Thus rolling again prob =

After rolling II time, if get 6, win otherwise lose.

Thus winning amounts A canbe

0     36   60

This is a genuine pdf since prob >0 and total prob = 1.

b)Expected gain = sum of gain * prob =

Thus I would be willing to pay an amount atmost 12 dollars.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i