# Out of 7 lottery tickets 3 are prize-winning tickets. If someone buys 4 tickets what is the probability of not winning any prize at all?

 10.66%
The probability of a ticket not containing a prize is $\frac{4}{7}$ so if someone buys 4 tickets and we want to know the probability of ticket 1 and ticket 2 and ticket 3 and ticket 4 not winning then we are asking for the following:
$p \left({t}_{1} \wedge {t}_{2} \wedge {t}_{3} \wedge {t}_{4}\right) = p \left({t}_{1}\right) p \left({t}_{2}\right) p \left({t}_{3}\right) p \left({t}_{4}\right)$ Since these are mutually exclusive events. Thus
(4/7)^4 = 10.66%