Question

In a manufacturing plant, there is a 10% chance that a stamp will be placed on a box upside down. The plant shipped 37 boxes today. What is the probability that 7 of the boxes have an upside-down stamp?

Answer 1

use the binomial for this one

Answer 2

7 upside down and 30 not upsides down, probability would be
\[P(x=7)=\binom{37}{7}(0.1)^7(0.9)^{30}\] and a calcualator

Answer 3

\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ x! }{ (y!)[(x - y)!] }\]where x! = (x)(x-1)(x-2) . . . (3)(2)(1)

\[\left(\begin{matrix}x \\ y\end{matrix}\right)\]is the number of ways you can select "y" elements from "x" objects. In this case, it is the number of ways you can select 7 boxes from the whole group of 37.\[\left(\begin{matrix}37 \\ 7\end{matrix}\right) = \frac{ (37)(36)(35) . . . (3)(2)(1) }{ [(7)(6)(5)(4)(3)(2)(1)][(30)(29)(28)...(3)(2)(1)] }\]

Answer 4

That will come down to (more easily):\[\left(\begin{matrix}37 \\ 7\end{matrix}\right) = \frac{ (37)(36)(35)(34)(33)(32)(31) }{ (7)(6)(5)(4)(3)(2)(1) }\]

Answer 5

so do i multiply 37 x 36 x 35?

Answer 6

Some calculators have probability and stats functions and buttons, and you can use those if you have them. If you have only a very basic calculator at hand, you can multiply it out, but it's not too hard, because it's only 7 numbers in the numerator and 7 in the denominator.

Your Windows operating system (if you are running Windows) has a scientific calculator that is super-easy to use.

Answer 7

No, my second post has 7 numbers in the numerator and 7 in the denominator. Then you have to finish up with the two factors that are to the 7th and 30th powers.

Answer 8

So, hopefully,\[\left(\begin{matrix}37 \\ 7\end{matrix}\right)\]which was the hard part is no problem for you now? @wequess2 ?

Answer 9

One other thing, and I see now why you asked a certain question above, the ellipses:

3 dots -> . . .

means a continuation, either into infinity (if nothing after the dots) or a termination at what comes after (with everything in between, "in pattern").

Answer 10

For example:

1 + 2 + 3 + . . . + 8 + 9 + 10

means:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

Answer 11

np. Look at my second post above for:\[\left(\begin{matrix}37 \\ 7\end{matrix}\right)\]On the right-hand side, it has 7 factors in the numerator and the denominator. That is self-explanatory. Multiply that out and get the fraction. You'll have to use a calculator. Once you have that, you multiply this by:

\[(0.1)^{7}(0.9)^{30}\]and you are completely done.