Answer to Question #344878 in Statistics and Probability for Akshay

Question

20% of the Chocos packets contain a free toy. Whats the probability youll need to open fewer than 4 packets before finding your first toy?

Answer 1

The formula for geometric distribution is

$$P(X=x)=(1-p)^xp$$

Given $p=0.2$

$$P(X<4)=P(X=0)+P(X=1)$$

$$+P(X=2)+P(X=3)$$

$$=(1-0.2)^0(0.2)+(1-0.2)^1(0.2)$$

$$+(1-0.2)^2(0.2)+(1-0.2)^3(0.2)$$

$$=0.2+0.16+0.128+0.1024=0.5904$$