# Probability

I used common sense, but how do you calculate this. If the stock market has a 65% probability of going up on any given day, what is the probability that one will observe at least 3 up days in a week? A. 23.5% B. 1.8% C. 42.3% D. 76.5%

wow… this one is good… least 3 up days means 3 up days — prob: 0.65^3*0.35^2=0.03364 4 up days — prob: 0.65^4*0.35=0.06248 5 up days — prob: 0.65^5=0.11603 Now adding up this numbers won’t make the final result, since 3 up days can be up,up,up,down,down or up,down,up,down,up… leads to the same result. use the combination formula to determine how many ways exist to obtain 3,4 or 5 up days. 3up: C= 5! / (5-3)! * 3! = 10 ways 4up: C=5! / (5-4)! * 4!=5 ways 5up: C=5! / (5-5)! * 5!=1 ways then multiply: 0.03364*10+0.06248*5+0.11603*1 = 0.7648 Answer D.

Answer is D. P(at least 3) = P(3) + P(4) + P(5) P(3) = 5C3 * 0.65^3 * .35 ^2 = 0.34 P(4) = 5C4 * .65 ^ 4 * .35 = 0.31 P(5) = 5C5 * .65 ^ 5 * .35^0 = 0.12 P(at least 3) = 0.34 + 0.31 + .12 = 0.77

You guys are good. I was totally blank when I looked at this Q. Correct answer is D.