The probability of winning one lottery ticket is 1/7. What is the probability of having bought 5 tickets to win

The probability of winning one lottery ticket is 1/7. What is the probability of having bought 5 tickets to win: a) for all five tickets; b) not a single ticket; c) at least one ticket.

Question A.

Let p be the probability that the next ticket will be winning.

By the condition of the problem, p = 1/7.

Five independent tests were carried out. Let’s find the probability that each of the five tickets will be winning.

P5 (5) = p ^ 5 = (1/7) ^ 5 = 1/16807 ≈ 0.00006 = 0.006%.

So, all five tickets will be winning with a 0.006% probability.

Question B.

Let q be the probability that the next ticket will not be winning.

q = 1 – 1/7 = 6/7.

Five independent tests were carried out. Let’s find the probability that none of the five tickets will win.

P5 (0) = q ^ 5 = (6/7) ^ 5 = 7776/16807 ≈ 0.46 = 46%.

So, none of the five tickets will be winning with a 46% probability.

Question V.

We will assume that event E will occur if at least one of the five tickets wins.

The opposite event Ē will happen if none of the five tickets are won. Answering the question “B”, we found out that the probability of the event Ē is equal to 7776/16807 (for calculations it is better to take the exact value, and not the approximate one).

Since the events E and Ē are opposite, the sum of their probabilities is equal to one. Moreover, P (Ē) = 7776/16807. Let us find the probability of event E.

P (E) = 1 – P (Ē) = 1 – 7776/16807 = 9031/16807 ≈ 0.54 = 54%.

So, at least one of the five tickets will be winning with a 54% probability.

Answer:

but. approximately 0.006 percent;

b. about 46 percent;

in. approximately 54 percent.