- 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**

A cup contains 4 pennies and 6 dimes. Three coins are selected with replacement from the cup. What is the probability that exactly 2 of the coins selected were pennies?

A. 0.288

B. 0.432

C. 0.712

**Explanation:**Since this is sampling with replacement, we use the binomial distribution with n = 3 and pai = 0.4. So, from the table, p(2) = 3!/[1! x 2!] x 0.4

^{2}x 0.6

^{1}= 0.288.

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**User Contributed Comments**
7

User |
Comment |
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Xocrevilo |
Possible to answer this one without calculation: Chance of picking a penny on the first try = 4/(4+6) = 40% As the coin is then replaced, the chance of picking a penny on the second try is also 40%. Therefore, the chance of picking two pennies in a row = 40% * 40%. Including the third pick, and the resultant probability is still less than 40% * 40%, which suggests that we exclude all the answers above 40%, at least, thus suggesting that the lowest answer (A) is correct. This methodology ignores the more complex calculations which we are meant to know for this exam, but logic is certainly useful for the probability questions. |

dlukas |
Good point; however, the TI BA II Plus will calculate nCr (and nPr) for you, and there will almost certainly be a question where you will need the formula. |

NNikolaiss |
Someone please explain - why n=3? |

Jurrens |
you're selecting 3 coins... n = 3 |

rsanfo |
pick penny is .4 pick dime is .6 pick penny + penny + dime is .4 * .4 * .6 = .096 there are 3 choose 2 ways to pick 2 pennies and 1 dime 3 * .096 = .288 |

ascruggs92 |
^I like that explanation. I guessed knowing the only value it could be was 0.28 because there's no way the probability would be higher than 40%. |

Emanco |
Thanks rsanfo |