The probability of winning $20 in a particular lottery is 0.05. What is the probability that you will get at least one $20 winner if you buy 90 tickets?
A) 0.010
B) 0.990
C) 0.950
D) 0.001

Question

The probability of winning $20 in a particular lottery is 0.05. What is the probability that you will get at least one $20 winner if you buy 90 tickets?
A) 0.010
B) 0.990
C) 0.950
D) 0.001

anonymous · Answer

what you want to do is compute the probability you get no winners, then subtract that number from one

anonymous · Answer

if the probability you win on any one ticket is $.05$ then what is the probability you do not win on any one ticket?

anonymous · Answer

.05?

anonymous · Answer

no that is the probability you win, not the probability you don't win

anonymous · Answer

Wouldn't the probability of you winning or losing be equal?

anonymous · Answer

not unless they are both $\frac{1}{2}$

anonymous · Answer

if the probability you win on one ticket is $.05$ then the probability you don't win is $1-.05=.95$

anonymous · Answer

so the probability you don't win on all 90 tickets is 
$$(.95)^{90}$$

anonymous · Answer

and therefore the probability you win on "at least one" ticket is 
$$1-(.95)^{90}$$