Asked by troy

It is known that 77% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 62 new products, find the following probabilities. (Round your answers to four decimal places.)

(d) within 2 years fewer than 10 succeed
Answered by Reiny
prob(fewer than 10 succeed) --> prob(none succeeds + one succeeds + 2 succeed + ...+ 9 succeed)
= (.77)^62 + C(62,1)(.23)(.77^61) + C(62,2)(.23^2)(.77^60) + ... + C(62,9)(.23^9)(.77^53)
= ....

lots of button-pushing here
Answered by troy
When I computed this, it came out very oddly.. The C is throwing me off. cNr?
Answered by Reiny
Yes
C(n,r) = <sub>n</sub>C<sub>r</sub>
= n!/(r!(n-r)!)

e.g. C(62,2) = 62!/(2!60!) = 1891

most calculators have the <sub>n</sub>C<sub>r</sub> key, mine is the 2nd function of the 5 key

e.g. to find C(62,2)

enter:
62
<sub>n</sub>C<sub>r</sub>
2
=

to get 1891

PS. I did not take the time to find the final answer to the above string of probabilities.
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