# Probability problem help

• Feb 27th 2010, 10:04 PM
masimini25
Probability problem help
There is a Probability of 0.15 that a particular type machine won’t start when first turned on. If the machine does not start on the first try, it overheats and the machine must be allowed to cool for 5 minutes before a second start attempt is made. There is a 0.88 probability that the machines do start on the second try. You are responsible for a group of 16 machines with these starting characteristics.
a) How many machines would you expect to start on the first try?

b) What is the probability that at least 10 machines will start on the first try?

c) If 8 machines start on the first attempt, what is the probability that exactly 5 additional machines start (after cool-down) on the second attempt?

my apporach
P(anB) = p(A/B) x P(B) p=o.15
p(s) = constant
1-n = 1-10 =9 N =10
• Feb 28th 2010, 07:16 AM
CaptainBlack
Quote:

Originally Posted by masimini25
There is a Probability of 0.15 that a particular type machine won’t start when first turned on. If the machine does not start on the first try, it overheats and the machine must be allowed to cool for 5 minutes before a second start attempt is made. There is a 0.88 probability that the machines do start on the second try. You are responsible for a group of 16 machines with these starting characteristics.
a) How many machines would you expect to start on the first try?

b) What is the probability that at least 10 machines will start on the first try?

c) If 8 machines start on the first attempt, what is the probability that exactly 5 additional machines start (after cool-down) on the second attempt?

my apporach
P(anB) = p(A/B) x P(B) p=o.15
p(s) = constant
1-n = 1-10 =9 N =10

a) The probability that any given machine starts on the first try is $0.85$. So the number to be expected to start on the first try is:

$N\times p=16 \times 0.85=13.6$

b) Use the Binomial distribution with $N=16$ and $p=0.85$

c) Use the Binomial distribution with $N=8$ (the number that did not start on the first try), and $p=0.88$

CB