John invites 12 friends to a dinner party, half of whom are men. Exact

Question

John invites 12 friends to a dinner party, half of whom are men.Exactly one man and one woman are bringing desserts. If one person from this group is selected at random, what is the probability that it is a woman OR a man who is not bringing a dessert?

A. 1/12
B. 1/4
C. 1/3
D. 5/12
E. 11/12

A. 1/12
B. 1/4
C. 1/3
D. 5/12
E. 11/12

Kinshook · Answer

# of men bringing desserts = 1
# of men NOT bringing desserts = 5
# of men = 6
# of women bringing desserts = 1
# of women NOT bringing desserts = 5
# of women = 6

# of favorable outcomes = 6 (# of women) + 5 (# of men NOT bringing desserts) = 11
# of total outcomes = 12

Probability = 11/12

IMO E

nick1816 · Answer

Answer should be 5/6 imo. 
Check the highlighted portion.

Lampard42 · Answer

Woman (6) or a man not bringing a dessert(5) is (6+5)/12 = 11/12

Archit3110 · Answer

total men = 6 and women = 6
desert being brought P ; 1/6 for men and 1/6 for women
P of desert ; 1/6+1/6 ; 2/3
no desert ; 1-2/3 ; 1/3
IMO C

CareerGeek · Answer

probability that it is a woman = 6/12
Probability of a man who is not bringing a dessert = 5/12

—> Required probability = 6/12 + 5/12 = 11/12

IMO Option E

Pls Hit kudos if you like the solution

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egmat · Answer

Let's break this down step by step.

First, let's understand the group: 
- Total people:  12 
- Men:  6 
- Women:  6 
- Exactly  1  man is bringing dessert
- Exactly  1  woman is bringing dessert

Now, the question asks: what is the probability of picking a woman OR a man who is NOT bringing dessert?

Let's count who qualifies: 
- ALL  6  women qualify (the question says "a woman" — it doesn't matter whether she's bringing dessert or not, she still counts)
- Men NOT bringing dessert:  6  total men minus  1  man bringing dessert =  5  men qualify

So favorable outcomes =  6  +  5  =  11

The ONLY person who does NOT qualify is the  1  man who IS bringing dessert. He's not a woman, and he's not a man who is NOT bringing dessert.

Probability =  11/12

Answer: E

The common mistake here is thinking women who bring dessert don't count.  But re-read the question carefully — it says "a woman OR a man not bringing dessert." The dessert condition only applies to the men. ALL women qualify regardless of dessert status.

Key principle:  In  OR probability  questions, always ask yourself — who is left OUT? Here, the only person excluded is the  1  dessert-bringing man. That's a much faster way to solve it:  12  -  1  =  11 , so  11/12 .

Amazingakhil · Answer

Total people = 12 → 6 men and 6 women.
1 man brings dessert → men NOT bringing dessert = 5.
Favorable = all women (6) + men not bringing dessert (5) = 11 people.
Total possible = 12 people.
Probability = 11/12

​

John invites 12 friends to a dinner party, half of whom are men. Exact

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John invites 12 friends to a dinner party, half of whom are men. Exact

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