# A probability with two conditions

• Jul 19th 2011, 11:07 AM
Selena
A probability with two conditions
Can someone please help me with this question? I *think* my logic is correct but I always get the wrong final answer. =/

Question: Given the following information concerning how many days a person has to wait for a repair:

(# of days, probability)
(1, 0.10) *means 10% chance to wait 1 day*
(2, 0.25)
(3, 0.30)
(4, 0.25)
(5, 0.10)

A random sample of 5 customers selected, what is the probaility that at least 4 people will have to wait more than 3 days?

I was trying to solve it by adding the probability of 4 people waiting more than 3 days to 5 people waiting more than 3 days, in other words P(4 people, day = 4, 5) + P(5 people, day = 4, 5) = [(5 select 4)(0.25 + 0.10)^4(1 - 0.25 - 0.10)^1] + [(5 select 5)(0.25 + 0.10)^5(1 - 0.25 - 0.10)^0], but that answer is wrong.
(sorry I'm not sure how to post those math symbols in picture format)
Can someone please enlighten me on this, thanks!
• Jul 19th 2011, 11:38 AM
Re: A probability with two conditions
Quote:

Originally Posted by Selena
Can someone please help me with this question? I *think* my logic is correct but I always get the wrong final answer. =/

Question: Given the following information concerning how many days a person has to wait for a repair:

(# of days, probability)
(1, 0.10) *means 10% chance to wait 1 day*
(2, 0.25)
(3, 0.30)
(4, 0.25)
(5, 0.10)

A random sample of 5 customers selected, what is the probability that at least 4 people will have to wait more than 3 days?

I was trying to solve it by adding the probability of 4 people waiting more than 3 days to 5 people waiting more than 3 days, in other words P(4 people, day = 4, 5) + P(5 people, day = 4, 5) = [(5 select 4)(0.25 + 0.10)^4(1 - 0.25 - 0.10)^1] + [(5 select 5)(0.25 + 0.10)^5(1 - 0.25 - 0.10)^0], but that answer is wrong.
(sorry I'm not sure how to post those math symbols in picture format)
Can someone please enlighten me on this, thanks!

You could alternatively calculate the probability of

1 person waiting less than 4 days
or nobody waiting less than 4 days.

See if the answers match up.
• Jul 19th 2011, 11:48 AM
Selena
Re: A probability with two conditions
Hmm why do I need to calculate 1 person waiting less than 4 days or nobody waiting less than 4 days? Those aren't complements to the two conditions given in the question right?
• Jul 19th 2011, 01:46 PM
Selena
Re: A probability with two conditions
LOL nevermind my solution is actually right. Minor calculation error with the selection!
Thanks anyways lol.