Each of the 75 professionals attending a conference is either a chef

Question

Each of the 75 professionals attending a conference is either a chef or a bartender, but not both. If a person is selected at random from the attendees, is the probability greater than 3/4 that the person selected will be a male chef ?

(1) There are 40 women at the conference.
(2) There are 20 chefs at the conference.

(1) There are 40 women at the conference.
(2) There are 20 chefs at the conference.

stne · Answer

(1) There are 40 women at the conference.

IF there are  40  women then there must be  35  men

If all of these men were chefs then max. probability of selecting a male chef  = \frac{35}{75}= \frac{7}{15} < \frac{3}{4}

We can answer NO.

SUFF.

(2) There are  20  chefs at the conference.

If all of these chefs were men then max. probability of selecting a male chef  = \frac{20}{75}= \frac{4}{15} < \frac{3}{4}

We can answer NO.

SUFF.
 
IMO D

talwarmeister · Answer

I think OA is wrong.

1. If there are 40 women then no of men =35. max probability of selecting a male chef at random would be when all men are chef, P= 35/75= .47 (approx) < 3/4
We can answer NO confidently that probability cannot be greater than 3/4.

2. There are 20 chefs at the conference. If all chefs are men then p= 20/75 which is less than 3/4
We can answer NO confidently that probability cannot be greater than 3/4.

Hence D

Bunuel · Answer

Sorry, there was a typo in the stem. The question should have been:  is the probability greater than  1/3  that the person selected will be a male chef ?  Edited. Can you try it now? Thank you!

stne · Answer

(1) There are 40 women at the conference.

If the  35   men all are chef then max probability  = \frac{35}{75}=\frac{7}{15}> \frac{1}{3}

We can answer Yes

If among the  35  men only  10  are chefs then probability  = \frac{10}{75}=\frac{2}{15}< \frac{1}{3}

We can answer NO

INSUFF.

(2) There are 20 chefs at the conference.

IF all the chefs are men then max. probability is  \frac{20}{75} =\frac{4}{15}< \frac{1}{3}

We can definitely answer NO.

SUFF.

Ans B

Hope it's clear.

Adnan123 · Answer

1/3 = 25/75
Are Male chefs > 25?

Statment 1
Total Women = 40
Total Men = 75 - 40 = 35

Amongst the men, Male chefs may or may not be greater than 25
Insufficient

Statement 2
Total Chefs = 20

Male Chefs cannot be greater than 25
Sufficient

KarishmaB · Answer

Responding to a pm:

Question: Is the probability greater than 1/3 that the person selected will be a male chef ?

When the question asked is 'is it greater than k' or 'is it less than k' or 'is it k' etc, info required is much less than anticipated. We don't need its actual value - just whether it is more or less or equal to k.

We don't need the probability of selecting a male chef here. Just whether the probability is greater than 1/3.

There are total 75 people.

(1) There are 40 women at the conference.

This means there are 35 men. If say all of them are chef, then probability of selecting a male chef is 35/75 which is more than 1/3. 
But if none of them are chef, then probability of selecting a male chef is 0/75 which is less than 1/3. 
Not sufficient alone.

(2) There are 20 chefs at the conference.

If all of them are male, then the probability of selecting a male chef is 20/75 which is less than 1/3. 
If none of them are male, the probability of selecting a male chef is 0/75 which is also less than 1/3. 
The point is that no matter how many of the 20 people are male, probability of selecting a male chef remains less than 1/3 because probability of selecting a chef itself is 20/75 which is less than 1/3. 
Hence this statement alone is sufficient to answer our question. It doesn't tell us how many male chefs there are but it does tell us that the probability of selecting one is less than 1/3.

Answer (B)

Each of the 75 professionals attending a conference is either a chef

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Each of the 75 professionals attending a conference is either a chef

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