Question

3. A lottery ticket can be purchased where the outcome is either a win or a loss. There is a 10% chance of winning the lottery (90% chance of losing) for each ticket. Assume each purchased ticket to be an independent event:
a) What is the probability of winning the lottery if 10 tickets are purchased? By winning, any one or more of the 10 tickets purchased result a win.

b) If you were to purchase lottery tickets in intervals of 10 (10, 20, 30, 40, 50, etc). How many tickets should you purchase to optimize you chance of winning. To answer this question, show a graph of probability of winning the lottery versus number of lottery tickets purchased.

Answer 1

Answer with Step-by-step explanation:

Since we have given that

Probability of winning the lottery = 10%

Probability of losing the lottery = 90%

a) What is the probability of winning the lottery if 10 tickets are purchased? By winning, any one or more of the 10 tickets purchased result a win.

Probability of winning atleast one of the 10 tickets is given  by

$1-P(\text{losing all tickets})\\\\=1-0.9^{10}\\\\=1-0.3486\\\\=0.6513$

b) If you were to purchase lottery tickets in intervals of 10 (10, 20, 30, 40, 50, etc). How many tickets should you purchase to optimize you chance of winning. To answer this question, show a graph of probability of winning the lottery versus number of lottery tickets purchased.

n               P(n)

10             0.6513

20            0.8784

30            0.9576

40           0.9852

50           0.9948

60           0.9982

70           0.9993

80           0.9997

90           0.99992

100          0.99997

So, the probability of winning the lottery versus number of lottery tickets purchased is shown below: