SOLUTION: 1. 1000 tickets are sold for a charity lottery at $5 each. 3 numbers are drawn out at random to receive 1st, 2nd, 3rd place prizes of $2000, $1000, and $500 respectively. (Like 124

Question 1072336: 1. 1000 tickets are sold for a charity lottery at $5 each. 3 numbers are drawn out at random to receive 1st, 2nd, 3rd place prizes of $2000, $1000, and $500 respectively. (Like 124, 321, & 996). What is the mean (expectation) from such a drawing?
2. A fair coin is flipped 6 times. What is is the probability of getting at least 2 heads? First figure out how many are in the sample space.
3. In a club there are 6 men & 8 women. A committee of four is to be chosen.
a.) how many possible committees are there?
b.) how many possible committees are there which have 2 men & 2 women?
4. A shipment of 100 DVD's has 5 which are defective. If you pick 2 at random (do not replace), what is the probability that they are all good (non defective)?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. 1000 tickets are sold for a charity lottery at $5 each. 3 numbers are drawn out at random to receive 1st, 2nd, 3rd place prizes of $2000, $1000, and $500 respectively. (Like 124, 321, & 996). What is the mean (expectation) from such a drawing?
Random "winnings":: 1995......995....495....-5
Probability:::::::: 1/1000...1/1000..1/100..997/1000
------------------------
E(x) = [1995 + 995 + 495 - 5*997]/1000 = -$1.50
----------------------------------------
2. A fair coin is flipped 6 times. What is is the probability of getting at least 2 heads? First figure out how many are in the sample space.
P(2<= x <=6) = 1 - binomcdf(6,0.5,1) = 0.8906
----------------------------------------
3. In a club there are 6 men & 8 women. A committee of four is to be chosen.
a.) how many possible committees are there?:: 14C4 = 1001
---------------------------------
b.) how many possible committees are there which have 2 men & 2 women?
Ans: [6C2*8C2]/14C4 = [15*28]/1001 = 0.4196
--------------------------------------
4. A shipment of 100 DVD's has 5 which are defective. If you pick 2 at random (do not replace), what is the probability that they are all good (non defective)?
And: 95C2/100C2 = 0.9020
-------------
Cheers,
Stan H.
---------------
RELATED QUESTIONS
1000 tickets are sold for a charity lottery at $5 each. Three numbers are drawn at random (answered by stanbon)

A raffle has $5 tickets and is selling 2000 of these tickets. The prizes are 1st place:... (answered by Edwin McCravy)

I really need help... I have a stomach virus and this quiz is due tonight. Can someone... (answered by user_dude2008)

A person has purchased 10 out of 1000 tickets sold in a raffle. To determine the 5 prize... (answered by ikleyn)

A lottery offers one 1000$ prize one 500$ prize and five 100$ prizes One thousand tickets (answered by Boreal,ikleyn)

A lottery has one $2000 prize, two $1000 prizes, and ten $500 prizes. Two thousand... (answered by edjones,jrfrunner)

Each year, readers of a certain magazine are asked to rank the top three best-dressed men (answered by Boreal)

Ten thousand lottery tickets are sold at $10 each. First prize is $10000. There are 3... (answered by CPhill)

A number greater than 3, given that the circle is yellow. There are 6 circles. The 1st... (answered by stanbon)