A lottery game advertises a jackpot of $41 million. The chances of a ticket having the winning numbers are 1 in 7.1 million. If Betty buys 10 lottery tickets, what are her chances of winning?
Please help me. Thank you
With ten tickets, the chances of winning are ten times higher than with one, or one in 710,000.
To calculate the chances of winning with 10 lottery tickets, you need to figure out the probability of not winning with one ticket and then subtract that probability from 1.
The chances of winning with one ticket are 1 in 7.1 million. Therefore, the probability of not winning with one ticket is 1 - (1/7.1 million).
To calculate the probability of not winning with one ticket, we'll need to convert 7.1 million to a decimal by dividing it by 1 million: 7.1 million / 1 million = 7.1.
So, the probability of not winning with one ticket is 1 - (1/7.1) ≈ 0.999999859.
Now, to calculate the probability of not winning with ten tickets, we raise the probability of not winning with one ticket to the power of 10. This is because each ticket is an independent event, and the probability of not winning with each ticket is the same.
(0.999999859) raised to the power of 10 = 0.999999859^10 ≈ 0.999999001.
Finally, to find the probability of winning with ten tickets, subtract the probability of not winning from 1:
1 - 0.999999001 ≈ 0.000001.
Therefore, Betty's chances of winning with 10 lottery tickets are approximately 1 in 1 million.