If the probability that Green Bay wins the Super Bowl is 1/12 and the

Question

If the probability that Green Bay wins the Super Bowl is 1/12 and the probability that Milwaukee wins the World Series is 1/20, what is the approximate probability that either Green Bay wins the Super Bowl or Milwaukee wins the World Series?

A. 1/240
B. 1/12
C. 1/8
D. 1/7
E. 4/3

Kudos for a correct solution.

A. 1/240
B. 1/12
C. 1/8
D. 1/7
E. 4/3

sterling19 · Accepted Answer

Winning the Super Bowl and winning the World Series are independent events; one outcome does not affect the other outcome.

P(A or B) = P(A) + P(B) - P(A and B) 
 P(A and B) = P(A) * P(B)

1/12 + 1/20 - (1/12 * 1/20)
= 5/60 + 3/60 - 1/120
= 8/60 - 1/120
= 16/120 - 1/120
= 15/120
= 1/8

The correct answer is C.

chetan2u · Answer

the two events being independent gives us P(super bowl,world cup)=not winning super bowl*winning world cup + winning super bowl*not winning world cup =19/20*1/12+1/20*11/12=30/240=1/8 ans C

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (C)

The probability of “X or Y” can be expressed as (Prob X) + (Prob Y) - (Prob of Both). In our case, this is 1/12 + 1/20 – (1/12 * 1/20), or 20/240 + 12/240 – 1/240, or 31/240, which is approximately 1/8.

iliavko · Answer

This one is mathematically strange,

If you use the formula  P(A or B)  you get 31/240

If you use the formula  P(A) * P(not B) + P(B) * P(not A)  you get 1/8 !!!

How is this possible?.. Both methods are correct I think and we get a different result?... (very close but math is an exact science, right?)

deepti1206 · Answer

Hi ,

As has been discussed above posts , P(AUB) = P (A)+ P (B)- P( Both A and B)

= 1/12 + 1/20 -( 1/12*1/20) 
 ~ 1/12 + 1/20 ( since 1/ 240 will be too small and considering less time duriing exam, we can ignore that) 
 ~ 32/240 = 2/15 = 0.13
 approximately equal to 1/8 ( 0.125)

So Answer is C.

Taulark1 · Answer

We can use conditional probability -

=  P(Green Bay wins)*P(Milwaukee doesn't win) + P(Green Bay doesn't win)*P(Milwaukee wins) 
= 1/12 * 19/20 + 11/12 * 1/20
=(19+11)/12*20 
=1/8 ( OPTION C )

PyjamaScientist · Answer

Experts,

Is conditional probability tested on GMAT?

Regor60 · Answer

People arriving at 1/8 as the exact answer are ignoring the outcome when BOTH occur, which is 1/240,and accounts for the exact answer of 31/240 instead of 30/240.

OR includes AnotB, BnotA and AB

Posted from my mobile device

bananachips · Answer

Aren't both events mutually exclusive?

Regor60 · Answer

No. Mutually exclusive means that two events can't occur together because they form part of a set comprising all the possible outcomes.

Green Bay winning the super bowl is one outcome of the separate set of outcomes related to the Superbowl.

Milwaukee winning the world series is an outcome of the world series.

Two different sets independent of each other.

manish8242 · Answer

Hello Regor60

Winning the cup will be either by A or B how can they both win together? in this case P(A and B) should be ) bcz only one of them will be the winner right? How can we say that both A and B can win at the same time with some (X) probability? Please clarify this.

Thanks

egmat · Answer

Great question! This is a common source of confusion that highlights the importance of reading GMAT problems carefully.

The Key Insight You're Missing:  These are  TWO COMPLETELY DIFFERENT sporting events :

The  Super Bowl  is the championship for American  football  (NFL) 
 The  World Series  is the championship for  baseball  (MLB)

They're not competing for the same trophy! Green Bay plays football, Milwaukee plays baseball. Both championships can absolutely happen in the  same year  - they're independent events.

Why P(A and B) ≠ 0:  Since these are different sports with different seasons and championships:
 
 Green Bay  can  win the Super Bowl in February 
 Milwaukee  can  win the World Series in October 
 Both can happen in the same calendar year!

Therefore:  P(A 	ext{ and } B) = P(A) 	imes P(B) = \frac{1}{12} 	imes \frac{1}{20} = \frac{1}{240}

Correct Solution:  Using the probability formula for "either/or":  P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B) 
 P(	ext{either wins}) = \frac{1}{12} + \frac{1}{20} - \frac{1}{240}

Converting to common denominator (240):  = \frac{20}{240} + \frac{12}{240} - \frac{1}{240} = \frac{31}{240} \approx \frac{1}{8}

Answer: C

Key Takeaway for GMAT:  Always identify whether events are:
 
  Mutually exclusive  (can't happen together) → P(A and B) = 0 
  Independent  (different events that can both occur) → P(A and B) = P(A) × P(B)

Your thinking would be correct if the question asked about two teams competing for the  same  championship!

If the probability that Green Bay wins the Super Bowl is 1/12 and the

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