- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

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**CFA Practice Question**

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 25 customers buy gasoline at this station.

What is the probability that no more than 20 pay in cash?

A. 0.1

B. 1.0

C. 0.9

**Explanation:**P(20) is almost zero. Probabilities of higher than 20 are also close to zero. So, the probability of not more than 20 is almost 1.

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**User Contributed Comments**
10

User |
Comment |
---|---|

danlan |
P(20)=C(25,20)*(0.4^20)*(0.6^5) |

chuong |
Accumulated probability |

george2006 |
use sigma=sqrt(n*pi*(1-pi)) it is 4 sigma away! |

anricus |
Is this not a binomial distribution since there are only two outcomes i.e. pay in cash or don't pay in cash? |

MUSK |
Danlan your equation is correct upto the extent that you are calculating P(20), but the answer requires 1- P(20) Watch out the word no more |

Profache |
You may use the binomial distribution for P(x<=20)which is equal to 1-P(x>20). But you will need to calculate P(21),P(22),P(23),P(24)and P(25), which can be time consuming. In this case, since the chances of more than 20 out of 25 customers paying cash is almost zero, then P(x<=20)=1 |

cslau83 |
0.9 is also almost one. |

viruss |
Sh&t ! I fell for it because I selected 0.9 only because I didn't want to select 100% probability ! This kind of stuff is nasty because it tricks you even if you understand what you are doing ... :s |

CJPerugini |
If we are talking significant figures 0.9 is more correct than 1.0. For C to hold true it would have to read 1, not 1.0. |

wahahachan |
Please don't harm the earth. 0.999999999 is not 1. Think before posting silly question. |