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Register now and save up to $200 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code ## OG-17 This topic has 4 expert replies and 0 member replies Joy Shaha Senior | Next Rank: 100 Posts Joined 05 May 2016 Posted: 59 messages Thanked: 3 times #### OG-17 Sat Nov 19, 2016 1:14 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur? A) 1/5 B) 2/5 C) 3/5 D) 4/5 E) 12/25 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2287 messages Followed by: 115 members Thanked: 1061 times GMAT Score: 770 Sat Nov 19, 2016 2:48 pm Joy Shaha wrote: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur? A) 1/5 B) 2/5 C) 3/5 D) 4/5 E) 12/25 If the probability that M will not occur is .8, the probability that it will occur is .2. If the probability that R will not occur is .6, the probability that it will occur is .4. So P(M) = .2 and P(R) = .4. P(M or R) = P(M) + P(R) - P(M and R). Because we're told that P(M and R) = 0, we have P(M or R) = .2 + .4 = .6 = 3/5. The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Matt@VeritasPrep GMAT Instructor
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Fri Nov 25, 2016 3:22 pm
It might be easier to see this using less abstract terms.

Suppose I told you that the Mariners have a 20% chance of winning the World Series, and that the Rangers have a 40% chance of winning the World Series. Since at most one of these teams could win, the probability that the Mariners OR the Rangers win = 20% + 40% = 60%.

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Sun Nov 27, 2016 5:51 pm
Joy Shaha wrote:
The probability that event M will not occur is 0.8 and the probability that
event R will not occur is 0.6. If events M and R cannot both occur, which of
the following is the probability that either event M or event R will occur?
A) 1/5 B) 2/5 C) 3/5 D) 4/5 E) 12/25
We are given that the probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6, and that events M and R cannot both occur.

We need to determine the probability that either event M or event R will occur.

The probability that event M will occur is 1 - 0.8 = 0.2 = 1/5

The probability that event R will occur is 1 - 0.6 = 0.4 = 2/5

Recall that the formula for the probability of event A or event B occurring is P(A or B) = P(A) + P(B) - P(A and B); therefore:

P(M or R) = P(M) + P(R) - P(M and R).

Since we are told that events M and R cannot both occur, that means P(M and R) = 0 and thus the probability that either event M or event R will occur is:

P(M or R) = 1/5 + 2/5 - 0 = 3/5.

Answer:C

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Jay@ManhattanReview GMAT Instructor
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Sun Dec 11, 2016 11:33 pm
Joy Shaha wrote:
The probability that event M will not occur is 0.8 and the probability that
event R will not occur is 0.6. If events M and R cannot both occur, which of
the following is the probability that either event M or event R will occur?
A) 1/5 B) 2/5 C) 3/5 D) 4/5 E) 12/25
Hi Joy,

Given that:

Probability of event M NOT to occur = P(M') = 0.8
=> Probability of event M to occur = P(M) = 1 - 0.8 = 0.2

Probability of event R NOT to occur = P(R') = 0.6
=> Probability of event R to occur = P(R) = 1 - 0.6 = 0.4

We are given that either of the two events can occur, thus,

(Probability of M to occur * Probability of R NOT to occur) + (Probability of M NOT to occur * Probability of R to occur)
= P(M)*P(R') + P(M')*P(R) = 0.2*0.6 + 0.8*0.4 = 0.12 + 0.48 = 0.60 = 3/5.

Hope this helps!

-Jay

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