Question 1062182: Could you help me please, to solve this problem
A lottery is created with 35 numbers. You have to pick all five numbers to win the grand prize. If this lottery is an example of sampling without replecemennt, what are the odds of any one $1 ticket winning? If this a state lottery , and the hrand lrize is $250.000, do you expect the state to make money? Explain.
From above question,calculate the odds of any sibgle ticket winning if the lottery is an example if sampling with replecement.
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Let's see how the first number from a ticket would match up to the winning number.
Your ticket has 5 possible numbers
The drawing is made for the 1st number, this can be 1 of 35 possible numbers.
Your chance of picking the first number correctly is therefore 5/35.
—
Now, on to the 2nd number. You have 4 more numbers on your ticket, and the drawing is made for the 2nd number. This 2nd number can only be 1 out of 34 (no replacement). So your chance of hitting the 2nd number is 4/34.
—
For the 3rd, 4th, 5th numbers you'll find the chances to be:
3rd: 3/33
4th: 2/32
5th: 1/31
—
So the overall chance of hitting all 5 numbers can be found by multiplying all the above fractions:
Chance of hitting all 5 numbers =
 =
 =
—
—
You would be expected to win once every 324632 times that you play, so if the prize is 250000 you will lose money over the long run. In real life of course it takes to long to play this many games, but if you ran a computer simulation to play 100's of millions of times you'd find that even if you win once in a while, over time you lose.
—
For sampling with replacement, the denominator does not change, you keep the denominator set to 35 for all 5 fractions. The numerator would still decrease by one for each number drawn.
—
|
|
|
