Question

A)In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.

Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.

1. PP(win) =    

A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.

1. Answer: $

A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.

1. Answer: $

B)There are nine female board members and twenty-one male board members.

i.How many ways are there to make a committee of eight board members?

ii.How many ways are there to make a committee of eight board members if exactly three must be female?

iii.Determine the probability of selecting a committee of eight board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.

C)Suppose a jar contains 8 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.

Answer:

Thank you :)

Answer 1

C)Here we can use hyper geometric distribution.

N= 46, total number of marbles

M= 8, number of red marbles

N-M=38,number of blue marbles.

n is the number of marbles to be drawn,

Let k be the number of red marblres in the marbles drawn.

                 

B)

i) No of ways a committee of 8 can be formed

ii) Number of ways where exactly three are females=

iii)P(selecting a committee where exactly 3 are females)=

                                                                                  =0.292

A) P(Win)=

P(loosing)=

   money you win if you win the lottery=1000000-2=999998

Money you lose if you don't win the lottery=-2

Your expectd gain form one ticket=

Your expected gain from 10000 tickets=

That is you tend to loose -19870$ from 10000 tickets

Expected value of the state from 10000 tickets 19870$

The state is expected to earn 19870$ from 10000 tickets.

You are expected to loose 19870$ from 10000 tickets.