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**CFA Practice Question**

You believe your broker makes profitable trades at a 50% rate (that is half the trades profitable, half unprofitable). In the last month your broker makes just 1 profitable trade out of a total of 3 trades. What is the probability that a broker with a probability 50% of making a profitable trade, would make 1 or less profitable trades out of a total of 3 trades?

A. 0.3333

B. 0.5000

C. 0.2500

**Explanation:**The probability of making 0 profitable trades is 1/8, the probability of making 1 profitable trade is 3 * 1/8. So the result is 1/8 + 3/8. Intuitively, the probability of one success should be the same as the probability of 1 failures, and the probability of 2 successes should be the same as the probability of 2 failures.

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**User Contributed Comments**
5

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

polanki |
where this 1/8 has come from |

bd1984 |
Polanki: P(0)+p(1) p(1)=3!/2!*(.5)^1*(.5)^2=.375 p(9)=3!/3!*(.5)^0*(.5)^3=.125 |

scottm8571 |
essentially it is zero tails on three coin flips, .5^3 or .125 1/8 |

Mikehuynh |
Good job bd1984 |

Scc0813 |
It can be done with the binomial probability formula. |