PrepSwift Probability Problem

GRE Quant Problem Solving
1

The image attached is a problem from the PrepSwift quiz under ‘choosing smart numbers’ in Quant Strategy. It is question 8 of 8.

image
image1068×625 35 KB

“The probability of event X happening given event Y happens is p. What is the probability that if Y happens five times, X does not happen at least once?”

My Answer:

  • P does not happen at least once = P never happens = (1-P)^5

Correct Answer:

  • 1-P^5

I am not sure why the probability of an event not happening at least once is not denoted as (1-p)^5 [my chosen answer] as opposed to 1-p^5 [the answer that is regarded as correct]

  • I thought 1-p^5 simply denotes the probability that something happens less than 5 times, while (1-p)^5 denotes something not happening at all (or not happening in five trials).
2

Although I am just on day 2 I guess treat the question this way.

P is the probability of x happening after each y happens. then if we do it 5 times, the probability is going to become p5.(Multiplication rule of probability and as we are considering the same event so they can be written in exponent form). You may ask why, for that you can simply do this logic on a dice.

Then as one is the summation of all probabilities, we can conclude that probability of the p5 not happening equals to,

1-(unfavourable probability that is p5) = 1-p5