SOLUTION: i don't know if you can really help me with this but i'll give it a go anyway... Records show that the probability is 0.60 that a stolen car in a certain suburb of NSW will be rec

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Question 194383: i don't know if you can really help me with this but i'll give it a go anyway...
Records show that the probability is 0.60 that a stolen car in a certain suburb of NSW will be recovered within one week.
(a) Find the probability that at least 7 of the 10 stolen cars will be recovered.
(b)Write down an expression for the exact probability that 15 of the 25 stolen cars will be recovered and use it to find this probability to 4 decimal places.
For (a), i got two answers from 2 attempts: 0.43670016 and 0.3823. I have no idea how to do (b).
HELP!!!
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Let x=.6 and y=.4 (not recovered within 1 week)
Now we expand the binomial (x+y)^10 an take the 1st four terms:
x^10=.0060
10x^9y=.0403
45x^8y^2=.1209
120x^7y^3=.2150
Sum of probabilities: .3823
.
b)
nCr best to find the number in front of the 15th term.
25C15=3268760
3268760x^15y^10=.1612
.
Ed