- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 5. Binomial Distribution

###
**CFA Practice Question**

A trial generates only two results, "success" and "failure." The probability of success is higher than that of failure. The variance of the number of failures in 20 trials equals 2.35. The probability of success on a given trial equals ______.

A. 0.136

B. 0.864

C. 0.452

**Explanation:**For a binomial distribution with N trials, with the probability of success = p in each trial, the variance equals Np(1-p). Hence, 20 x p x (1 - p) = 2.35. Solving this quadratic equation gives p = 0.136 or p = 0.864.

###
**User Contributed Comments**
9

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

DAS11 |
Should be q=.136 (prob of failure), then p=.864 (prob of success). right? |

dimos |
right! |

PedroEdmundo |
No need to calculate, sinceP has to be greater than 0.50 and only B is greater than that. |

andy4cfa |
Remembe the formular: variance = Np(1-p) |

labsbamb |
right pedro p is higher than q hence p>0.5 The only choice is B |

cfaeater |
Could someone just please state the formula to calculate this rather than just guessing? Do we need to rearrange the formula np(1-p)? If so how does this rearranged formula look? |

poomie83 |
yes variance and number are given so you have to solve for probability of success/failure |

shwade |
Is there a calc. shortcut for the quad. equation on the BA II Plus |

CJHughes |
Would appreciate it if someone could break down the quadratic equation. Thanks |