Question

If a person buys one ticket of a State lottery, then the probability that he wins a price is 0.11. If a person buys one ticket each month for five months, what is the probability that he will win least one price?

Answer 1

The probability that he wins at least 1 ticket is 0.4416.

Step-by-step explanation:

Given:

The probability of winning is, $P(W)=0.11$

So, probability of losing is, $P(L)=1-P(W)=1-0.11=0.89$

Now, let 'E' be the event of him losing all 5 months.

Let 'W1' be the event of him winning a price in at least 1 month.

Therefore, probability of losing all five months is given as:

$P(E)=P(L)\times P(L)\times P(L)\times P(L)\times P(L)=(0.89)^5=0.5584$

Now, in order to win in at least one month, we subtract P(E) from 1.

Therefore, probability of winning for at least one month is given as:

$P(W1)=1-P(E)=1-0.5584=0.4416$

So, the probability that he will win least one price is 0.4416.