Answer to Question #305428 in Statistics and Probability for knowledge

Question

suppose that you are searching for a room for rental at makweng until you find a place that will satisfies your needs. Suppose that the probability of finding the right place is 0.4. what is the probability that you do not choose at least the forth room of the rooms you have checked.

Answer 1

The probability that we choose the room $p = 0.4$ ; the probability that we don't choose the room $q = 1-p=1-0.4=0.6; X -$the number of the chosen room.

If we choose the first of the checked rooms: $P(X=1)=p=0.4;$

the second: $P(X=2)=q\cdot p=0.6\cdot0.4 = 0.24;$

the third: $P(X=3)=q^2\cdot p=0.6^2\cdot0.4 = 0.144;$

the fourth: $P(X=4)=q^3\cdot p=0.6^3\cdot0.4 = 0.0864.$

The probability that we choose one of the four inspected rooms:

$$P(X\leq4)=P(X=1)+P(X=2)+P(X=3)+P(X=4)=$$

$$=0.4+0.24+0.144+ 0.0864=0.8704.$$

The probability that we do not choose any of them:

$$P(X>4)=1-P(X\leq4)=1-0.8704=0.1296$$