Source: Revised GRE PDF 2nd Ed. Section 5; #23 (p. 82)

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# A certain experiment has three possible outcomes

A certain experiment has three possible outcomes. The outcomes are mutually exclusive and have probabilities p, p/2 and p/4, respectively. What is the value of p ? 1/7, 2/7, 3/7, 4/7, 5/7

### 3 Explanations

14

wait so, if the question didn't state that the outcomes are mutually exclusive, and this was a comparison question the answer would be D (the provided information is insufficient)?

Apr 4, 2018 • Comment

Cydney Seigerman, Magoosh Tutor

Now, you've proposed a question that changes a few aspects of the original problem. So, let's take a look at these parts one by one.

if the question didn't state that the outcomes are mutually exclusive

If the outcomes are not necessarily mutually exclusive, then we cannot definitely say that the probabilities of the three outcomes add to 1.
Let's take a look at the two changes you've made to the original problem:

1. If the question didn't state that the outcomes are mutually exclusive

If the outcomes are not necessarily mutually exclusive, then we cannot definitely say that the probabilities of the three outcomes add to 1.

2. [if] this was a comparison question

Now, here, we need to clarify what we are comparing. We can compare the probabilities of the three outcomes:

p > p/2 > p/4

However, we cannot determine the exact value of p. So, we would not be able to determine the relationship between p and a concrete value. So, the answer would be D (insufficient info) if the question asked us to compare p with a value such as 2/3, given that the outcomes are not necessarily mutually exclusive.

I hope this helps :)

1

Annie Wang

which magoosh lessons in probability should I watch to review for this problem?

Dec 9, 2017 • Comment

Sam Kinsman

Good question! These are 3 complementary events. It might be helpful to watch the video on complementary events (https://gre.magoosh.com/lessons/138-complementary-events-and-simple-rules). The lesson on mutually exclusive events might also be helpful (https://gre.magoosh.com/lessons/139-mutually-exclusive-events).

1

Chris Lele

Sep 27, 2012 • Comment