Question

Dave is the manager of a construction supply warehouse and notes that 60% of the items purchases are heating items, and 15 % are plumbing items. Find the probablility that at least three out of the next five items purchased are heating items. Some one please help its urgents, and oh Happy New Years!

Answer 1

at least 3, this is not going to be that quick

Answer 2

Its alright I just really dont understand this question, ill pay attention though

Answer 3

you have to compute exactly 3, exactly 4, exactly 5 and exactly 6 and add them up
OR
you have to compute exactly 0, exactly 1 and exactly 2, add them up and subtract the total from 1

Answer 4

oh three out of FIVE i should learn to read,
in any case you will have to compute three probabilities

Answer 5

the probability that all 5 are plumbing items is the easiest, it is
\[P(x=5)=(.15)^5\] that is five times in a row you got plumbing items

Answer 6

the probability that you get exactly 4 plumbing items is
\[P(x=4)=4\times (.15)^4\times (.85)\]

Answer 7

that is, you get exactly 4 plumbing items, exactly 1 not plumbing item, and there are 5 different ways to get that
damn i made a typo sorry let me fix is
replace the 4 by a 5

Answer 8

\[P(x=4)=5\times (.15)^4\times (.85)\]

Answer 9

finally the probability you get exactly 3 is
\[P(x=3)=10\times( .15)^3\times (.85)^2\]

Answer 10

compute these three numbers, add them up, and that will give you the probability that you get at least 3

Answer 11

ok I will, but its the set up your using a formula? Because i remember my teacher using a long formula

Answer 12

the formula for this binomial probability is this
if you have \(n\) trails, with the probability of success in any one trial as \(p\) and therefore the probability of failure is therefore \(1-p\) then the probability you get exactly \(k\) successes in \(n\) trials is
\[P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}\]

Answer 13

in your case we used \(n=5\), \(p=.15\) and \(1-p=.85\) but we had to compute for \(k=3, k=4,k=5\)

Answer 14

note that \(\binom{5}{3}=10\) and \(\binom{5}{4}=5\)

Answer 15

\(p=0.6\) for heating items, \(q=0.4\) for non-heating items

Answer 16

when i do .15^5 i get a weird number on my calculator? DO you have the same?

Answer 17

so it is
my answers were for plumbing because i can't read

Answer 18

OH NO!!! Lol we screwed up

Answer 19

\[P(x=3)=10\times (.6)^3\times (.4)^2\]
\[P(x=4)=5\times (.6)^4\times (.4)\]
\[P(x=5)=(.6)^5\]

Answer 20

http://www.wolframalpha.com/input/?i=10%28.6%29^3%28.4%29^2%2B5%28.6%29^4%28.4%29%2B%28.6%29^5