You bought 12 raffle tickets that are good for 4 raffles. If 715 total tickets were sold what is the probability that you will win at least 1 of the raffles?

Question

asked Sep 1, 2021 223k views

1 Answer

Sujivasagam · Answer 1 · 2021-09-05T19:53:31+0000

Answer:

0.06546.

Explanation:

Total number of tickets = 715

Good raffle tickets (Prize) = 4

Number of tickets bought = 12

$\text{Probability of winning}=\frac{\text{Number of tickets bought}}{\text{Total raffle tickets}}$

$\text{Probability of winning}=(12)/(715)$

$\text{Probability of not winning}=1-(12)/(715)=(703)/(715)$

Let x be event of the number of winning prizes.

Probability that you will win at least 1 of the raffles is

$P(x\geq 1)=1-P(x=0)$

$P(x\geq 1)=1-^(4)C_0\left((12)/(715)\right)^0\left((703)/(715)\right)^(4-0)$

$P(x\geq 1)=1-\left((703)/(715)\right)^(4)$

$P(x\geq 1)=1-0.93454$

$P(x\geq 1)=0.06546$

Therefore, the required probability is 0.06546.