Question

Suppose the probability that a randomly selected​ man, aged​ 55-59, will die of cancer during the course of the year is startfraction 300 over 100 comma 000 endfraction 300 100,000. how would you find the probability that at least 1 man out of​ 1,000 of this age will die of cancer during the course of the​ year?

Answer 1

The probability that a randomly selected man dies of cancer during the course of the year = $\frac{300}{100000}= \frac{3}{1000}=0.003$

The probability that a randomly selected man does not die of cancer during the course of the year = $1-0.003=0.997$

The probability that atleast one man of this age dies of cancer is the complement of the probability that no man dies of cancer. In equation form we can write:

Probability that atleast one man of this age dies of cancer =  1 - No man at this age dies of cancer

The probability that no man dies of cancer out of 1000 selected men = $(0.997)^{1000}=0.04956$, rounded of to 5 decimal places

Thus the probability that atleast one man at this age dies of cancer = 1 - 0.04956 = 0.95044