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## 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
3

#### OG-17

Sat Nov 19, 2016 1:14 pm
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

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
890 messages
Followed by:
18 members
470
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

_________________
Manhattan Review GMAT Prep

Locations: New York | Mumbai | Ho Chi Minh City | Budapest | and many more...

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
501 messages
Followed by:
3 members
43
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
890 messages
Followed by:
18 members
470
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

_________________
Manhattan Review GMAT Prep

Locations: New York | Mumbai | Ho Chi Minh City | Budapest | and many more...

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
501 messages
Followed by:
3 members
43
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

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