What is the probability that on a given workday Mr. Jonathan dresses

Question

What is the probability that on a given workday Mr. Jonathan dresses in formals, travels by car to his office, and drinks a coffee there?

(1) Jonathan dresses in formals on alternate days, and drinks coffee each day he wears formals.

(2) Jonathan goes to his office by car 3 of every 5 days.

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stne · Answer

(1) Jonathan dresses in formals on alternate days, and drinks coffee each day he wears formals.

We still do not know two things considering only work days:
 
(i) Whether the days are Mon, Wed and Fri or Tue and Thu?
(ii) On which days does he travel by his car to office?

Without these info. statement is  INSUFF.

(2) Jonathan goes to his office by car 3 of every 5 days.

We do not know whether he dresses in formal , drinks coffee these same days that he drives to office .

INSUFF.

1+2

We still do not know on which days he does all three of these tasks.

INSUFF.

Hope it's clear.

Ans E

DamanDeep · Answer

Probability of (Formals) : 1/2
Probability of (Coffee/Formals) : 1
Probability of (going to office by car) : 3/5

As all are mutually exclusive / independent events.
Probability : (1/2 * 1 * 3/5) = 0.3

What is problem in the solution ?

yashhw · Answer

Why do we need to know specific days of him dressing formal or going to office by car? can't we simply calculate the probability of Mr. Jonathan doing those things on a random day?

RohanNewDelhi · Answer

do we assume monday - friday as workdays even if it is not explicitly mentioned? as diff companies, diff countries have diff workdays

FrozenDragon · Answer

No, we don’t need to assume specific workdays like Monday to Friday. The term “workday” is just a generic reference and does not affect the probability calculation.
 
 The real issue is that we are not given any relationship between dressing in formals and traveling by car. Because of this missing information, the required probability cannot be uniquely determined. Hence, the correct answer is E.

egmat · Answer

Hi RohanNewDelhi,

That's a sharp thing to notice, and the good news is you don't have to settle it. The "workday" definition turns out to be a red herring here: whether a workday means Mon-Fri, a 6-day week, or anything else, it has  no effect  on the answer.

Here's why. On the GMAT you never import outside facts about how companies or countries schedule their weeks. You only use what the statements give you. And what makes this question  E  has nothing to do with naming the days - it's that we never learn whether the three events land on the  same  days.

The real gap

The statements hand you three separate frequencies:

- Formals: half the days, and coffee on every formal day
- Car:  3  of every  5  days

But "how often" is not "on which days." To get the probability of all three happening  together , you'd need to know how the car days overlap with the formal days - and nothing tells you that.

Two cases that both fit - and disagree

Take  10  days. Formals on  5  of them, car on  6  of them ( 3/5 ).

-  Maximum overlap:  all  5  formal days are also car days, so all three happen on  5  days, probability  5/10 = 1/2 
-  Minimum overlap:  car days avoid formal days as much as possible, so only  1  day has all three, probability  1/10

Same statements, two different answers. That's the textbook signal for  not sufficient  - and it holds no matter how you define a workday. So the combination fails.

This is also why the earlier " 1/2  x  1  x  3/5  =  0.3 " reply doesn't hold: multiplying the probabilities quietly assumes the events are independent, which the problem never tells us.

Answer: E

What is the probability that on a given workday Mr. Jonathan dresses

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What is the probability that on a given workday Mr. Jonathan dresses

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