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

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**CFA Practice Question**

The probability that the price of a stock increases is 0.30. The price of the stock will either increase or decrease each day independently of what happened on the previous day. An experiment consists of observing the price of this stock during a 30-day period. What is the probability that the stock price will increase 10 days out of the 30 days?

A. 0.03

B. 0.1416

C. 0.3333

**Explanation:**The number of days that the stock price increases over this period follows a binomial distribution with 30 trials, a probability of success (increase in stock price) equal to 0.30 and a probability of failure (decrease in stock price) equal to 0.70. Therefore, the parameters of the distribution are n = 30 and p = 0.3. The probability that the number of successes is 10 out of 30 trials is: p(10) = 0.1416.

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**User Contributed Comments**
7

User |
Comment |
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yikes |
30c10 * 0.3^10 * 0.7^20 =0.1401 |

tanyak |
what's 30c10? |

xjarl |
It's the binomial coefficient. (30!/(10!*20!)) |

chamad |
tanyak: It's the combination(combinatorial) formula nCr |

Marinov |
Does anybody know the function in the calculator that can handle these large numbers? |

GBolt93 |
for hp12c the factorial button (n!) is g, 3. So the buttons for 30!/10!20! would be 30, g, 3, 10, g, 3, 20, g, 3, x, / |

mcbreatz |
2nd + (Plus Symbol) for the BAII. Format in this case would be 30 2nd + 10. |