- 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**

Which of the following is not a binomial experiment?

B. Rolling a die 3 times and letting x count the numbers of 2s obtained.

C. Randomly selecting a ball (with replacement) three times from a jar containing 1, 2, 2, 5, 6, and 7, and letting x count the number of 2s obtained.

D. Randomly selecting 3 balls from a jar containing balls numbered 1, 2, 2, 5, 6, 7 and letting x count the number of 2s obtained.

A. Flipping a coin 3 times and letting x count the number of heads obtained.

B. Rolling a die 3 times and letting x count the numbers of 2s obtained.

C. Randomly selecting a ball (with replacement) three times from a jar containing 1, 2, 2, 5, 6, and 7, and letting x count the number of 2s obtained.

D. Randomly selecting 3 balls from a jar containing balls numbered 1, 2, 2, 5, 6, 7 and letting x count the number of 2s obtained.

Correct Answer: D

For "randomly selecting 3 balls from a jar containing balls numbered 1, 2, 2, 5, 6, 7 and letting x count the number of 2s obtained," we do not have independent events. So, this is not a binomial experiment. We can find the probability distribution for random variable x using a tree diagram (we can not use the binomial formula).

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**User Contributed Comments**
10

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

wanger |
what's 2s? |

songshow |
what is difference with B.C.D |

tengo |
only d changes the experiment so that it is no longer independent. Since the 3 balls are not replaced in the jar after each trial the probabilities for the second trial are not equal to the probabilities of the first trial |

danlan |
It's similar to 3 |

chamad |
Another way to get answer D is that there is only two 2s. So D is impossible as you'll never get 3 balls! |

Meka76 |
I like chamad's answer...thanks! |

magicchip |
Key is no replacement. |

bundy |
Replacement is key |

mjwoulf |
chamad - you can still draw 3 balls, there is just a 0% chance of 3 balls being 2s. Yup, replacement. |

praj24 |
Two Twos, nah!?! |