M04-09

Question

The probability that a visitor at the mall will purchase a pack of candy is 30%. If there are three visitors at the mall today, what is the probability that exactly two of them will buy a pack of candy?

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

Show Answer

Official Answer

C

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

Bunuel · Accepted Answer

Official Solution:

The probability that a visitor at the mall will purchase a pack of candy is 30%. If there are three visitors at the mall today, what is the probability that exactly two of them will buy a pack of candy?

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

Show Answer

Official Answer

C

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

When examining the event where exactly 2 out of 3 visitors purchase a pack of candy, there are  \frac{3!}{2!} = 3  possible scenarios: (Buy, Buy, Not Buy); (Buy, Not Buy, Buy); and (Not Buy, Buy, Buy). The calculation  \frac{3!}{2!} = 3  represents the number of permutations of the pattern BBN (Buy, Buy, Not Buy).
 
Furthermore, each "Buy" event has a probability of 0.3, while each "Not Buy" event has a probability of  1 - 0.3 = 0.7 . Therefore, the probability of having exactly 2 out of 3 visitors buy a pack of candy is given by  P(B=2) = \frac{3!}{2!} *0.3^2 *0.7 = 0.189 .

Answer: C

Bunuel · Answer

We are multiplying by 3 because the case when two out of three buys candy can occur in three different ways: BBN (first buys, second buys, third does not buy), BNB, NBB.

Check different approaches  HERE  and  HERE .

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations 
 PS questions on Combinations

Tough and tricky questions on Combinations

Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability 
 Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.

mrinal0308 · Answer

Ans C
In the simplest way : 
 apple08  ,  Bunuel : 
P(Buying candy)=0.3
So, P(Not buying)=0.7
There are 3 people and we need to chose exactly 2 who buy it. 
So, 
0.3*0.3*0.7 (Bcz other person would not bu has to be taken into consideration here)
=0.063

We can do this is 3 ways, different selections. 
therefore, 0.063*3 =0.189

CPGguyMBA2018 · Answer

I have a question.

I calculated my answer by simply (0.3)(0.3)(0.7) = 0.063
and got the wrong answer.

I thought this was the way we calculate probabilities...
Now, do we multiply by 3 because we are asked for the possibility that  EXACTLY  two people out of three buy candy?

If we were to be asked a question without the mentioning of EXACTLY, would it make any difference?

In what cases can we just multiply the possibility of outcomes and what cases do we have to multiply the result by the total possible outcomes, which in this case is 3?

Thank you!

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

yazadsarkari · Answer

I think this is a  high-quality  question.

Chrisharley · Answer

I like the solution - it’s helpful.

M04-09

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