Answer: (a) 0.02373
(b) 0.9854
(c) 0.9990
Step-by-step explanation:
This is a binomial experiment , because the events are independent, the probability of each trial remain constant.
Let P be the probability that they have land lines and q be the probability that they do not have land line, that is
P = 0.75
q = 0.25
From binomial distribution formula,
P(X=r) = nCr
![q^{n-r}](https://tex.z-dn.net/?f=q%5E%7Bn-r%7D)
(a) p ( all the 5 have land lines) = 5C5 ![0.75^{5}](https://tex.z-dn.net/?f=0.75%5E%7B5%7D)
![0.25^{0}](https://tex.z-dn.net/?f=0.25%5E%7B0%7D)
= 1 x0.02373 x1
= 0.02373
(b) p ( at least one of them has land line) = 1 – p( 0ne of them has)
P( one of them has ) = 5C1 ![0.75^{1}](https://tex.z-dn.net/?f=0.75%5E%7B1%7D)
![0.25^{4}](https://tex.z-dn.net/?f=0.25%5E%7B4%7D)
= 5 x 0.75 x 0.00390625
=0.01465
Therefore p ( at least one of them has land line) = 1-0.01465
= 0.9854
(c) p ( at leats one of them does have ) = 1 – p( 5 of them does not)
P( 5 0f them does not) = 5C5 ![0.25^{5}](https://tex.z-dn.net/?f=0.25%5E%7B5%7D)
![0.75^{0}](https://tex.z-dn.net/?f=0.75%5E%7B0%7D)
= 1 X 0.0009765625
= 0.0009765625
Therefore , p ( at least one of them does have ) = 1 - 0.0009765625
= 0.9990