On the average, only 1 person in 1000 has a particular rare blood type. How many people would have to be tested to give a probability greater than 1/2 of finding at least one person with this blood type?

• 663
• 683
• 693
• 705
• 725

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: C

If [math]n_0[/math] people are tested then the number of people with a particular rare blood type has a binomial distribution with [math]n=n_0, p=0.001 [/math]. We need to find the smallest [math]n_0[/math] such that

[[math]] P(N \geq 1) = 1 - (1-p)^{n_0} \geq 1/2 \implies n_0 \geq \frac{\log(1/2)}{\log(1-p)} = 692.81 [[/math]]

Hence the answer is [math]n_0 = 693 [/math].