A student is entering in a college housing lottery for 2

A student is entering in a college housing lottery for 2 consecutive years. What is the probability that the student receives housing through the lottery for at least 1 of these years?

(1) Eighty percent of the students in the lottery do not receive housing through the lottery in any given year. This means that the probability of not receiving housing is 0.8. P(receiving housing for at least 1 of 2 years) = 1 - P(NOT receiving housing for both years) = 1 - 0.8^2. Sufficient.

(2) Each year, 1 of 5 students receives housing through the lottery. The same info as above: the probability of not receiving housing is 4/5 = 0.8. Sufficient.

Answer: D.

Hope it's clear.
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Is the answer D??

Probability that the student receives housing through the lottery for at least 1 of these years=
P( Receiving the house in Year 1)*P( Receiving the house in Year 2) +P( Receiving the house in Year 1)* P( Not Receiving the house in Year 1) +P( Not Receiving the house in Year 1)*P( Receiving the house in Year 2)

Both statements tell us that P( Receiving the house in Year)=1/5 and so P( Not Receiving the house in Year)=1-1/5 = 4/5

So Probability that the student receives housing through the lottery for at least 1 of these years=

1/5*1/5+1/5*4/5+4/5*1/5 =9/25

Both sentences are telling you that the chance of a positive outcome is 20% in a given year. To win in at least one year out of two is the same as calculating (1 - not winning at all) = (1- 0.8*0.8).

Bunuel Can you please explain it.

Hi All,

This DS question tests your knowledge of the 'concept' of Probability, without actually requiring that you do any math.

We're told that a student is entering a college housing lottery for 2 consecutive years. We're asked for the probability that the student receives housing through the lottery for AT LEAST 1 of these years?

To answer this question we need to know either the probability of getting housing in each of the 2 years OR the probability of NOT getting housing in each of the 2 years.

1) Eighty percent of the students in the lottery do not receive housing through the lottery in any given year.

This fact tells us that 80% of students do NOT get housing in ANY given year, meaning that the probability of getting housing is the SAME each year. Knowing that 80% DON'T get housing means that 20% DO get housing. Thus, we COULD calculate the probability of getting housing at least once in 2 years (but we don't have to).
Fact 1 is SUFFICIENT.

2) Each year, 1 of 5 students receives housing through the lottery.

This Fact tells us the exact SAME information that Fact 1 did - 20% get housing. We already know that Fact 1 is SUFFICIENT, so Fact 2 is also (for the same reason).
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Stat 1: Probability that don't receive the lottery is 80/100 => 4/5

Now probability that will receive the lottery is 1-4/5 =? 1/5...Sufficient.

Stat 2: 1/5...Sufficient..

IMO option d.

There are 4 possible scenarios: Y1,Y2; Y1,N2; N1,Y2; N1,N2 (Y1 = Got housing in year 1, N1 = Didnt get in year 1, etc)
To calculate "at least 1 of these" = 1-[(N1)(N2)]

Statement 1: N=80% = 4/5
so, 1-(4/5)(4/5) = 9/25

Statement 2: essentially says the exact thing as statement 1.

So, Option D.

Hope it helps

I believe the answer is A

Statement 1: 20% of students "in" the lottery will get housing. So we can find the probability
Statement 2: say 1 in 5 receives housing through the lottery but doesn't say how many apply for the lottery. I meant it to read that if they are 10 students 2 get housing from the lottery but the students that apply could be 2,3,4, or 5 so insufficient

20% = 20/100 = 1/5
Statement 1 & 2 are the same except for the way of saying it.
Also, by the same logic that you applied to discard S2, we can discard S1 as well. Let's say 4students applied. @0% of 4 is 0.8, which can't be the number of students.
It is a must to note here that 20% and 1/5 do not represent a number that will apply on every number in the possible set, as in, not every fifth student gets the room. S1 presents the fact in % terms, while S2 can be said to have mentioned the same in terms of probability.

Hope it helps

its D

Both statements are sufficient individually to determine the probability for 1 year

Saying 1/5 students "in" the lottery receives housing from lottery and saying 1/5 students receive housing from lottery are two different statements. the first one says that for every 5 people in the lottery 1 gets housing (so we can calculate probability) the second states that 1 in 5 of total students in the lottery or outside the lottery receive housing from lottery. and it doesn't state that all students enter the lottery

OK, so you were asking something completely different. Sorry I didn't get that earlier.
In questions such as these (P&C), rarely(if any, at all) you are allowed to bring external information. Some set theory question allow bringing in of additional info.
Here, for example and as per my understanding, if the college has 100 students, all 100 are participating in the lottery. Unless and until explicitly mentioned, or hinted by the options, you should not think that a certain number of students are not participating.
This can be clarified only when the OA is published.

Please Bunuel

I solved this question incorrect, and I want to understand why my rationale is wrong.

I chose A.
I thought that statement 2 is insufficient because we don't know the probability that a student receives a housing lottery in both years.
I tried to apply: (probability of year 1 + probability of year 2) - Both + Neither = 1 ---> (and what is between brackets is what we should calculate)
I draw a tables, where the green area is what to calculate.

Statement 1: it is clear that the green area is 20%, so probability is \(\frac{1}{5}\)

statement 2: I thought that the green area could range between 20% to 40%, so insufficient.

I wish my question is clear,
Thanks in Advance.

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