Is the probability that Patty will answer all of the questio

Note that conceptually the question is fine for GMAT but the calculations involved make it unsuitable. You can use approximation but I don't think GMAT will give you such a question.

P(Answering all questions correctly) = P(Answering each question correctly)^n
where n is the number of questions.

Say if there are two questions, P(Answering all questions correctly) = P(Answering first question correctly) * P(Answering second question correctly)


1) for each question on the chem. exam, patty has a 90% chance of answering the question correctly.
We don't know the number of question yet. Not sufficient

2) There are fewer than 10 questions on patty's chem. exam.
We don't know the probability of answering questions correctly. We also don't know the exact number of questions. Not sufficient.

Using both together,

P(Answering all questions correctly) \(= (0.9)^n\)
We know that n is up to 9. Now check using approximation:

\((.9)^ = .81\)
\((.9)^3 = (.9)*(.8) = .72\)
\((.9)^4 = (.9) * (.9)^3 = (.9)*(.7) = .63\) (Ignore 2 of the .72 and use only .7)
\((.9)^5 = (.9)*(.6) = .54\)
\((.9)^6 = (.9)*(.5) = .45\)

Note that using approximation, \((.9)^6\) came out to be less than 50%. The powers of 9 will not deplete as fast as we have approximated since we only took the first digit after decimal. But we do get the idea that soon enough powers of .9 will go below 50%. Perhaps it will go less than 50% on the 7th power.
So depending on the number of questions, the probability of answering all questions correctly can be more than 50% or less than 50%.

Answer (E)

Thanks, I had not solved for all values of 9^x.. Assuming they will not deplete that fast..

Is the probability that Patty will answer all of the questions on her chemistry exam correctly greater than 50%?

(1) For each question on the chemistry exam, Patty has a 90% chance of answering the question correctly.
(2) There are fewer than 10 questions on Patty's chemistry exam.

Opt1).
Probability the she answers correctly,
P(C) = 0.9
therefore, probability for wrong answer, P(W) = 0.1

if number of questions on the test is 2, then P(C) = (0.9)^2 = 0.81
--------------------------------------------3------------- = (0.9)^3 = 0.729

examine the pattern , Probability of getting correct answers will reduce with the increase in number of questions

since no information about the number of questions is provided, this option is not sufficient.

Opt.2)
there are fewer than 10 questions. This is still not sufficient as no information about the probability of correctly answering the question is provided. It can be 1, 0.5, 0.9 or anything.
Not sufficient.

opt1 & opt2 together are still not sufficient.
if number of questions is 4 , P(getting all correct) = (0.9)^4 = ~0.64

this probability will decrease with the subsequent increase in the number of questions.
Hence, both statements together are not sufficient.

Answer. E

I will go with E.

1 - doesn't tell much. if there are 2,3,4 questions then yes, the probability is >50% but if more than 5 ...I don't think so... since we do not know how many questions there are, we cannot answer the question.
2 - well, this doesn't tell much, so not sufficient.

1+2
if there are 4 questions, then the answer is yes, the P>50%. but if there are 7+ then no, the P<50%.

E

Let's phrase what we are looking for:

Let's assume that all the questions are independent from each other, and that each question have an euqal chance to be solved by Patty - lets denote the chance to solve correctly with P.

In addition, let's denote the number of questions in the test with N

So, the question asks to find out if (p)^n>0.5.

St1.
- since 0.5 = 5/10, we can see that (9/10)^2 will be greater than 5/10 only for n=1. if n>1, the answer will be no.

St.2
Based on the mentioned above this statment does not give us any new information.

To conclude-> answer is E.

DS: probability that Patty will answer all of the questions on her chemistry exam correctly > 50% ?

Statement 1: P(correct answer) = 0.9
NOT SUFFICIENT

Statement 2: For <10 question probabilities can be P = (0.9)^9, 0.9^8......, 0.9^2, 0.9

Now 0.9 = 0.9
.9^2 = 0.81
.9^3 = 0.729 ~ 0.73
.9^4 ~ 0.73 * .9 = .657
.9^5 ~ .657*.9 = .5913 ~.59
.9^6 ~ .59 * .9 = .531 ~ .53
.9^7 = .53*.9 = .477

So, values above .5 and below .5 exists. Hence NOT SUFFICIENT

i miss the word "fewer"
so there could be 4 questions, or there could be 7 questions
it yields to difference possibility.

DS questions are the best. Before answering the question, Probability = Favorable number of outcomes / Total number of outcomes

From 1) P(answering question correctly) = 0.9, P(answering question incorrectly) =0.1

We are not given, Total number of outcomes, Insufficient

from 2) fewer than 10 can be 2,3,4,5,6,7
Not sufficient

Even after combining we would not get a definite answer

E
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________