A student majoring in accounting is trying to decide on a number of firms to which he should apply. Given work experience and grades, he can expect to receive a job offer from 70% of the firms to which he apllies. The student decides to apply to four firms. What is the probability he receives no job offers?


Let $p$ be the probability that student receive a job offer. Given that $p=0.7$. The student decides to apply to four firms, thus $n=4$ number of firms where student apply for a job. Let $X$ denote the number of job offers receives to the student.

Here $X\sim B(4, 0.7)$.

The probability mass function of $X$ is
$$ \begin{aligned} P(X=x) &= \binom{4}{x} (0.7)^x (1-0.7)^{4-x},\\ &\quad x=0,1,\cdots, 4. \end{aligned} $$

The probability that the student receives no job offers is

$$ \begin{aligned} P(X= 0) &= \binom{4}{0}(0.7)^0(1-0.7)^{4}\\ & = 0.0081 \end{aligned} $$

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