Probability

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Probability

by BTGmoderatorRO » Sat Nov 11, 2017 8:30 am

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

OA is c

I solved this question twice and I got two answers, can someone confirm if it is C or A

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Source: Beat The GMAT — Problem Solving | Sat Nov 11, 2017 8:30 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sun Nov 12, 2017 9:17 am

Hello Roland2rule.

The question tell us that the probability that event M will NOT occur is 0.8, it implies that the probability that event M will OCCUR is 0.2.

Also, as the probability that event R will NOT occur is 0.6, then the probability that event R will OCCUR is 0.4.

Finally, it is asked what is the probability that either event M or event R will occur, so, the probability is the sum of the two probabilities calculated before. That is to say,
$$P\left(M\right)+P\left(R\right)=0.2+0.4\ =\ 0.6\ =\ \frac{3}{5}.$$

So, the correct answer is C .

I hope this can help you.

Feel free to ask me again if you have a doubt.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 26, 2019 7:38 am

BTGmoderatorRO 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

OA is c

I solved this question twice and I got two answers, can someone confirm if it is C or A

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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