Given : A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 25 cents each, find the expected winnings for a person buying 1 ticket.

To find : What are the expected winnings?

Solution :

There are one first prize, 2 second prize and 20 third prizes.

Probability of getting first prize is $\frac{1}{20000}$

Probability of getting second prize is $\frac{2}{20000}$

Probability of getting third prize is $\frac{20}{20000}$

A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each.

So, The value of prizes is

$\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10$

If 20000 tickets are sold at 25 cents each i.e. $0.25.

Remaining tickets = 20000-1-2-20=19977

Probability of getting remaining tickets is $\frac{19977}{20000}$

The expected value is

$E=\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10-\frac{19977}{20000}\times 0.25$

$E=\frac{1000+600+200-4994.25}{20000}$

$E=\frac{-3194.25}{20000}$

$E=-0.159$

Therefore, The expected winnings for a person buying 1 ticket is -0.2.

3 0

3 years ago

The probability that it will snow in a certain town on January 1st is 0.29 find the probability that in a given year it will not

Mashutka [201]

Answer:

0.71

Step-by-step explanation:

The probability is a chance of an event happening. The probability of assured event is 100% or 1.

If there is no chance of an event happening the probability is zero (0).

The probability of snowing = 0.29

The probability of not snowing = 1 - 0.29

= 0.71

5 0

3 years ago