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**CFA Practice Question**

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least ten pay in cash?

A. .586

B. .575

C. None of these answers

**Explanation:**This is a binomial distribution: n!(p

^{r})(q

^{(n-r)})/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6

P(10) = 25!(0.4

^{10})(0.6

^{15})/10!15! = 0.1612

P(11) = 25!(0.4

^{11})(0.6

^{14})/11!14! = 0.1465

P(12) = 0.1140

P(13) = 0.0760

P(14) = 0.0434

P(15) = 0.0212

P(16) = 0.0088

P(17) = 0.0031

Summing up we get close to 0.574.

We can continue until r = 25 but the probability gets smaller and converges to 0.575.

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**User Contributed Comments**
27

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

shasha |
any faster way to avoid time-consuming calculation? |

Bira |
I would never lose time on this one. |

mm04 |
The answer seems to be questionable. What it shows is that the probability for 'exactly' 10 people paying cash...the question asks 'at least' ten paying cash...I noticed the answer but did not choose it because of this 'at least'... |

johnny |
mm04: the answer and explanation show clearly "at least" 10, not as you said. |

sireklove |
For anyone else who hasn't noticed yet, the BA II has keys for factoral, combination, and permutation formulas. See the 2nd functions on "x", "-", and "+". I just noticed them today for the first time. |

Rguerra |
It took me about 10 minutes to do this one. |

mtcfa |
Use this formula for each; the BAII Plus has the formula built in: nCr x p^r x (1-p)^n-r. Use it on each and add up. |

MUSK |
can any one PLEASE explain where this formula is built in BAII Plus ????? |

julamo |
I knew what formula to use, but it seemed so impossible to be asked for such time-consuming calculations that I ended up assuming there had to be a clever faster way to do it... not even... whoever can solve that question in less than 1.5 minutes deserves a medal... |

Adkins |
Some questions will take 10 mins, others will take 10 secs. It all averages out to 120 questions in 3hrs. Don't stress out if one question takes a long time, because others will be fast. DO NOT look at your watch for every question but only every 10-20 questions. Thanks mtcfa for the shortcut but still have to do each one manually and add them up. |

dealsoutlook |
this one is a pretty long one..i agree with adkins, i will try not to look at my watch..but i doubt i wont be stressing :( |

cwest020 |
instead of doing 10-25 could you do 1-9 and then subtract from 1? that could save some time. |

shiva5555 |
That's what i did took about 3 minutes with the calculator. |

arudkov |
wasted my time. another way - P(guess)- 33,33%. So, good probability. dont agree w Adkins - NO MORE than 60 seconds. Check time every 20 seconds. |

arudkov |
Mechanics - 5s - read question, 20s - read summary, 25s - do the job, 5s - check. If no answer - GUESS and go go go! |

pporres |
It gives no additional benefit to make thousands of calculations. The point here is to understand the mechanics |

MaresaJaden |
Even if you know the concept skip it and go. Come back at then end if you have time. |

amyjones |
Is there not a way to do this on the 12C? |

Mikehuynh |
Agree with Adkins |

ShanikaJ |
no all you have to do on the BA II plus is 25 2nd nCR 10 to get the combination formula, whiich is 3,268,760. Then multiply this by the product of 0.4 to the 10th power and 0.6 to the 15th power. |

Friso |
cwest020 and others, it is faster to do the 1 - the rest variant, but don't forget the chance of 0! In this example, you would have to do 10 calculations: 1 - P(0) ~ P(9) instead of the 16 of P(10) ~ P(25) |

Procbaby1 |
Shanika did you even try that? That's only the first step. |

tijean25 |
Anyone notices there are only 2 possible answers . That is a 50% probability of guessing this right and move on to the questions that make sense if this ever show up in the exam |

praj24 |
I did (0.4^10) + (0.6^15) * 100 = 0.575 |

farhan92 |
the method highlighted by praj seems to work -better than guessing too. |

GBolt93 |
pretty sure that's only a coincidence. |

cfastudypl |
Is not a coincidence, just appreciate praj24 efforts. Thanks praj24. |