If six people decide to come to a basketball game, but three of them are only 2/5 sure that they will stay for the entire time (the other three are sure they'll stay the whole time), what is the probability that at the end, at least 5 people stayed the entire time?

MathCuber
Aug 14, 2018

#3**+2 **

Solution:

\( \text {Three of the six will remain at the game until its conclusion, this leaves three (3) }\\ \text {with a 40% probability of remaining at the game until its conclusion.}\\ \text {Find the probability that two (2) or more of these three (3) will remain. }\\ \text {To find this probability, calculate the Binomial CDF for } \large \rho \small (X \geq 2, 0.40)\\ \large \binom{3}{2}*0.4^2*0.6^1 + \binom{3}{3}*0.4^3 = 0.352\\ \;\\ \text {The probability is } 35.2\%\\ \)

GA

GingerAle
Aug 15, 2018