Question

Astudent applies for a summer intenatsp at 6 omerent companies. Geen this studenes previos work epenence and gades, there-a30% dance oe gettig an one company does not affect getting an ofter from another company. What is the probability this student will receive 1 or more offers (Round to 3 decimal places eratary company. Geting offer from

Answer 1

Solution:

   We are given that : a student applies for a summer internship at 6 different companies. Thus n = sample size = 6
Also we are given that : there is a 30% chance of getting an internship offer at any company and getting an offer from different companies are independent.

Thus X = Getting number of offers from companies follows Binomial distribution with n = 6 and p = 0.3

We have to find :

Probability that this student will receive 1 or more offers=..........?

That is :

$P(X\geq 1)=.......?$

Thus

$P(X\geq 1)=1-P(X<1)$

$P(X\geq 1)=1-P(X=0)$

Thus find P(X=0) by using Binomial probability formula :

$P(X=x) = _{n}C_{x}\times p^{x}\times q^{n-x}$

where

$_{n}C_{x}=\frac{n!}{x!\times (n-x)!}$

and q = 1 - p = 1 - 0.3 = 0.7

Thus

$P(X=x) = _{n}C_{x}\times p^{x}\times q^{n-x}$

$P(X=0) = _{6}C_{0}\times 0.3^{0}\times 0.7^{6-0}$

$P(X=0) =\frac{6!}{0!\times (6-0)!}\times 1\times 0.7^{6}$

$P(X=0) =\frac{6!}{1\times 6!}\times 1\times 0.117649$                ( Since 0! = 1 )

$P(X=0) =1 \times 1\times 0.117649$

Thus

$P(X\geq 1)=1-P(X=0)$

$P(X\geq 1)=1-0.117649$

$P(X\geq 1)=0.882351$

$P(X\geq 1)=0.882$

Thus the probability that this student will receive 1 or more offers is 0.882 .