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

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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Hi All,

This prompt tells us three Probability-based pieces of information:
1) The probability that Event M will NOT occur is 0.8
2) The probability that Even R will NOT occur is 0.6
3) Events M and R CANNOT BOTH occur.

We’re asked for the probability that Event M OR Event R will occur. While these types of probability questions are generally a bit harder in terms of difficulty, this particular prompt includes “causality” (which is a really rare concept in the Quant section) that actually makes the question easier to solve.

Normally, individual probabilities have NO impact on one another, but in this prompt, we are told that if Event M happens, then Event R CANNOT happen (meaning that there is an ‘absolute’ here and nothing to calculate). The same situation occurs if Event R happens (re: Event M automatically does NOT happen and there’s nothing to calculate).

Thus, there are just a couple of simple calculations to work through:

-The probability that Event M happens is 1 – 0.8 = 0.2
-The probability that Event R happens is 1 – 0.6 = 0.4

Thus, the probability that EITHER will happen is 0.2 + 0.4 = 0.6

Final Answer: C

GMAT Assassins aren’t born, they’re made,
Rich