Posted by **troy** on Friday, October 21, 2011 at 7:03pm.

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

- statistics, find the probability -
**Reiny**, Friday, October 21, 2011 at 7:37pm
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

- statistics, find the probability -
**troy**, Friday, October 21, 2011 at 7:57pm
When I computed this, it came out very oddly.. The C is throwing me off. cNr?

- statistics, find the probability -
**Reiny**, Friday, October 21, 2011 at 8:14pm
Yes

C(n,r) = _{n}C_{r}

= n!/(r!(n-r)!)

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

most calculators have the _{n}C_{r} key, mine is the 2nd function of the 5 key

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

enter:

62

_{n}C_{r}

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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