Answer to Question #193164 in Statistics and Probability for rumeysa

Question

1)   Traffic lights with a turning arrow are red 60% of the time. If you approach 5 lights in a row, find the probability of stopping:

a.     Exactly three times.

 

 

 

 

b.    At least two times.

 

Answer 1

Solution:

Given, $p=60\%=0.6, q=0.4,=5$

$X\sim Bin(n,p)$

(a) $P(X=3)=^5C_3 (0.6)^3(0.4)^2=0.3456$

(b) $P(X\ge2)=1-P(X<2)=1-[P(X=0+P(X=1)]$

$=1-[^5C_0 (0.6)^0(0.4)^5+^5C_1 (0.6)^1(0.4)^4] \\=0.91296$