### 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
Explanation: This is a binomial distribution: n!(pr)(q(n-r))/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6

P(10) = 25!(0.410)(0.615)/10!15! = 0.1612
P(11) = 25!(0.411)(0.614)/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.

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?