Statistics problem: I have a dozen batteries 5 are dead. What's the probability that the first 4 I choose work

Question

The answers are in the back of the book and it says the answer is 0.071. I just need to know how to get to the answer so i know how to do it on the test. Thanks!

Answer 1

Hi Emily. The odds of the first battery not being dead are 7/12, which equals 0.583.

There are now 11 batteries left, so the odds of the 2nd battery not being dead are 6/11, which equals 0.545.

There are now 10 batteries left, so the odds of the 3rd battery not being dead are 5/10, which equals 0.500.

There are now 9 batteries left, so the odds of the 4th battery not being dead are 4/9, which equals 0.444.

If you now multiple these odds of picking a good battery (a battery that is not dead) for the first four tries you get: (0.583)(0.545)(0.500)(0.444) = 0.0706 = 0.071.

Hope this helps you. Best wishes and good luck!

Answer 2

you have 12 batteries
out of them 5 are dead s0 7 work (12-5 = 7)
lets say your drawing the batteries out of a bag so your total is 12 and you have to draw 4 times and each time they have to be working batteries:

7/12 *6/11*5/10*4/9 = 0.07

each fraction looks like this:
the # of working batteries\ total batteries in the bag

you have to subtract the batteries each time (the working ones and the total)

good luck on your test!

Answer 3

A number of people have shown you one way to get the answer.

There is another way. You need to divide the number of ways that you can choose four of the seven good batteries by the number of ways that you can choose for of the twelve batteries.

The combinations of seven batteries taken four at a time is Combin(7,4) = 7!/(4!*3!) = 35. So -- there are 35 different combinations of four good batteries that you can choose.

You need to divide this by the number of combinations of 12 things taken four at a time. This is Combin(12, 4) = 12!/(4!*9!) = 495

The probability is then 35/495 = 0.070707...

Answer 4

Multiply the chances that at each selection of a battery you pick a functional one, by each other.

7/12 x 6/11 x 5/10 x 4/9 = 840/11880 = 0.07070707.....