- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

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**CFA Practice Question**

There are five multiple-choice questions on an exam, each with responses a, b, c, or d. Each question is worth 5 points and only one option per question is correct. Suppose a student guesses the answer to each question. His or her guesses from question to question are independent. If the student needs at least 20 points to pass the test, the probability that the student passes is closest to ______.

B. 0.0010

C. 0.0156

A. 0.0146

B. 0.0010

C. 0.0156

Correct Answer: C

X, the number correct if you were guessing, is binomial with parameters n = 5 and p = 0.25. To get at least 20 points, the student must get at least 4 of the 5 questions correct. Choice A is the probability of getting exactly 4 correct and choice B is the probability of getting exactly 5 correct. The correct answer is P(X >= 4) = P(X = 4) + P(X = 5).

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**User Contributed Comments**
19

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

moma20 |
p=0.25 because there is only 1 correct choice from the 4 choices |

manessa |
can some explain how to arrive at the answer plz |

RichWang |
P(4) = 5C4 * ( 0.25 ^ 4 ) * (0.75 ^1) = 0.0146 P(5) = 5C5 * ( 0.25 ^ 5 ) * (0.75 ^0) = 0.0010 P(4)+P(5)=0.0156 |

Rivermax |
good question |

CFAonTheBrain |
this is going to be on the test im sure |

hillrat |
what is 5C4 on the calculator, in fact what the heck is it? |

anneki |
its for combination: 5 2nd + 4 |

cslau83 |
If we are only concern about passing, then shouldn't a direct calculation on x=4 be sufficient? Why do you need to add on the probability of getting all 5 correct?? |

dhess0 |
Anyone know how to do combination on hp12c? |

jorgeman81 |
in the BAII I input 5 2nd + 4 and I get 5, any idea what I'm doing wrong? |

jayj001 |
5 2nd nCr 4 = |

mjwoulf |
jorgeman81, 5ncr4 does equal 5 in english this means there are 5 ways to get 4 our of 5, i.e. 1234 1235 1245 1345 2345 |

mjwoulf |
jorgeman81, 5ncr4 does equal 5 in english this means there are 5 ways to get 4 our of 5, i.e. 1234 1235 1245 1345 2345 |

Kaloyan |
Instructions on how to calc. nCx problems with HP12c are given on the bottom on the page h20000.www2.hp.com/bizsupport/TechSupport/Document.jsp?cc=us&taskId=120&prodSeriesId=33525&prodTypeId=215348&objectID=c01910446 |

Kaloyan |
better try with google, typing in and looking for "HP 12c Financial Calculator - Statistics - Rearranging Items" |

kondagadu |
don't understand why it has to be X>=4 , why not just x=4 ? |

johntan1979 |
To all those questioning x>=4... READ the last part of the question... "the probability that the student PASSES" If it were asking for the probability that the student AT LEAST passes, then it should be only x=4 |

davcer |
student passes, so is the probability of getting 20 0r 25 points in the exam |

alexmon83 |
hits too close to home, ahem. |