There are 10 phones in a rural area The number of phones bei

There are 10 phones in a rural area. The number of phones being used simultaneously is a random variable. The usages of the phones at different different days are independent independent.

Find: a. The probability that on a five days period, at 9AM, the number of phones being used is more than three

. b. The probability that on one or more days of the five days at 9AM, the number of phones being used is less than or equal to two.

Solution

let X be the random variable denoting the number of phones being used simultaneously.

there are all total 10 phones.

the usage of phones at different days are independent.

si X has the pmf-- f(x)=1/10   x=1,2,3,.........,10

a) P[number of phones used in each day >3]=P[X=4]+P[X=5]+....+P[X=10]=7/10

P[number of phones used in five days >3]=7⁵/10⁵ [answer]   [as the usage of phones at different days are independent.]

b)P[number of used in each day <=2]=P[X=1]+P[X=2]=2/10

P[number of phones used in one or more of five days<=2]=2⁵/10⁵ [answer]