Probability question!

Question

Your chances of winning on a Florida Lottery scratch off ticket is one out of five. Suppose you buy 8 tickets in one day. What is the probability that:

a. You win on all 8

b. You lose on all 8

c. You get at least one winner

I know this is a simple question but I really don't remember how to exactly do it. Thank you for any help!

Answer 1

Hi Alexis, please see below for an explanation. The independence rule here is a key thing to remember, which enables you to multiply the probabilities by one another.

a. P(Win All) = (0.2)^8 = 0.00000256

For an individual win, the probability is 1/5 or 0.2. Thus, by the independence rule, you would do (0.2)^8 to account for the probability across all 8 of the trials.

b. P(Lose All) = (0.8)^8 = 0.16777216

For an individual loss, the probability is 4/5 or 0.8. Thus, by the independence rule, you would do (0.8)^8 to account for the probability across all 8 of the trials. This is similar to part A but on the loss side instead of the win.

c. P(Win At Least One) = 1 - P(Lose All) = 1 - 0.16777216 = 0.83222784

The last part is most easily solved knowing that the total probability sums to 1. Thus, the rule of subtraction can be used where the probability of an event is equal to 1 minus the probability of that event's complement (where the complement is the chance of the event not occurring). Thus, P(Win At Least One) = 1 - P(Lose All), where P(Lose All) was previously solved in Part B.

I am happy to help more with this problem or others from your course, so please let me know if you would like to schedule a lesson. I look forward to hearing from you!