Suppose that 10,000 tickets are sold in one lottery and 5000 in another. if a person buys 100 tickets in each lottery, what is the chance she will win one first prize?

a. 0.0098

b. 0.0298

c. 0.0002

d. 0.0300

100 tickets are purchased in each lottery.

The chance of winning the first price in the 10,000-tickets lottery is

100/10000 = 10⁻²

The chance of winning the first price in the 5,000-tickets lottery is

100/5000 = 2 x 10⁻²

The two purchases are independent events, therefore the chance of winning the first price is

10⁻² * (2 x 10⁻²) = 2 x 10⁻⁴ = 0.0002

Answer: c.

The probability is 0.0002