Given that a student applies for a summer internship at 5
different companies. Given this student's previous work experience and
grades, there is a 40% chance of getting an internship offer at any
company. Getting an offer from one company does not affect getting an
offer from another company.
What is the probability this student will receive 2 or more offers? (Round to 3 decimal places.)
This situation describes a binomial distribution with the probability of success = 40% = 0.4 and the number of trials = 5.
P(2 or more offers) = P(2) + P(3) + P(4) + P(5) = 1 - [P(0) + P(1)]
The binomial probability is given by
[tex]\bold{P(x)=\ ^nC_xp^x(1-p)^{(n-x)}} \\ \\ \bold{P(0)}=\ ^5C_0(0.4)^0(1-0.4)^{(5-0)} \\ \\ =1\times1\times(0.6)^5=0.07776 \\ \\ \bold{P(1)}=\ ^5C_1(0.4)^1(1-0.4)^{(5-1)} \\ \\ =5\times0.4\times(0.6)^4=2\times0.1296 \\ \\ =0.2592 \\ \\ \bold{P(0)+P(1)}=0.07776 + 0.2592=0.33696 \\ \\ \bold{\therefore P(2\ or\ more\ offers)}=1-[P(0)+P(1)] \\ \\ =1-0.33696=0.66304[/tex]
Therefore, the probability this student will receive 2 or more offers is 0.663 to 3 decimal places.
