Question

2.
Fill in the Blank: When producing ball bearings, the probability that one is too small is .20, the probability that a bearing is marred is .17, and the probability that a bearing has both defects is .02. Find the probability that a ball bearing has neither defect.

3.
Fill in the Blank:
You roll two dice, one red and one green. Find the probability that at least one of the die is a 2 given that the total of the dice is 8.

Answer 1

whoa nelly which one do you want to do first?

Answer 2

whichever..doesn't matter! :)

Answer 3

probability it has one defect or another or both is
\[.20+.17-.02\] as it is the same as \[P(A\cup B)=p(A)+P(B)-P(A\cap B)\]

Answer 4

compute that number, then subtract it from 1 to get your answer

Answer 5

so I got .65 for the answer.

Answer 6

second one we do by counting
there are the ways to get an "8"
\[\{(2,6),(3,5),(4,4),(5,3),(6,2)\}\] so your sample space contains those 5 pairs
count the number that have one die as a 2, your answer will be clear

Answer 7

i think your arithmetic is wrong on the first one

Answer 8

.81 for the first one?

Answer 9

oh no sorry, my arithmetic is wrong!!

Answer 10

it was \(.65\) you were right the first time, sorry

Answer 11

ok great

Answer 12

second one clear?

Answer 13

i'm confused on the second one

Answer 14

you are given that the total is 8 right?

Answer 15

yes

Answer 16

so i wrote what the possibilities are
it is this:
\[\{(2,6),(3,5),(4,4),(5,3),(6,2)\}\]

Answer 17

those are the only 5 possible ways to get an 8 if you roll two dice
hope it is clear what those ordered pairs represent, the green die, and the blue die

Answer 18

then you count, out of those 5 possibilities, how many contain a 2 ?

Answer 19

2

Answer 20

right. so your answer?

Answer 21

2

Answer 22

oh no! you are looking for a probability,

Answer 23

you forgot your denominator

Answer 24

2/5?

Answer 25

yes

Answer 26

which would be .4?

Answer 27

yes it would, if you like decimals

Answer 28

i hope you look over the work we just did and convince yourself that it is really easy, especially the second one. just a matter of counting really

Answer 29

thank you for your help.