Question

Internet sites often vanish or move, so that references to them can't be followed. Supposed 13% of Internet sites referenced in major scientific journals are lost within two years after publication. If a paper contains five Internet references, what is the probability that all five are still good two years later

Answer 1

Answer:

The probability that all five are still good two years later is 0.498.

Explanation:

Let X = number of internet sites that vanishes within 2 years.

The probability of an internet site vanishing within 2 years is: P (X) = p = 0.13.

A paper consists of n = 5 internet references.

The random variable X follows a Binomial distribution with parameters n = 5 and p = 0.13.

The probability mass function of a Binomial distribution is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2,3...$

Compute the probability of X = 0 as follows:

$P(X=0)={5\choose 0}(0.13)^{0}(1-0.13)^{5-0}=1\times 1\times 0.498421\approx0.498$

Thus, the probability that all five are still good two years later is 0.498.