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16 Sep 2014, 00:22
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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
A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027
16 Sep 2014, 00:22
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Bookmarks
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
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
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
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
27 Jan 2017, 07:18
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conneryeon001
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.
