Question

PLEASE HELP ME WILL : "A bicycle manufacturer is studying the reliability of one of its models. The study finds that the probability of a brake defect is
4 percent and the probability of both a brake defect and a chain defect is 1 percent. If the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect?"

Answer 1

Consider drawing a Venn diagram?

Answer 2

So would chain defect would be 6?

Answer 3

No... The problem says:
P(chain defect) OR P(brake defect) = 6
P(chain defect) AND P(brake defect) = 1
P(brake defect) = 6
P(chain defect) = 6 - 4 - 1 = 1

Answer 4

So it will be 1?

Answer 5

The Venn Diagram which @luffingsails has drawn above is a really good way of visualising this problem. The key probability formula which we need to use here is:

\[P(B~or~C) = P(B) + P(C) - P(B~intersect~C)\]

where B is the probability of a brake defect and C is the probability of a chain failing.

Answer 6

okay so that formula what is it for?

Answer 7

P(B} = 0.04
\[\large P(B\cap C)=0.01\]
\[\large P(B\cup C)=P(B)+P(C)-P(B\cap C)\]
0.06 = 0.04 +P(C) = 0.01
P(C) = 0.06 - 0.04 + 0.01
P(C) = 0.03 or 3%

Answer 8

So would it be 3%?

Answer 9

Yes, the probability of a chain defect is 3%,

Answer 10

Thank you to all three of you guys

Answer 11

So, rearranging the above formula, the probability of a chain failing is:

\[P(C) = P(B~or~C) - P(B) + P(B~intersect~C)\]

I think there's a little mistake in the Venn diagram....it should be:


We know that P(B) = 0.04 overall, P(B or C) = 0.06 and P(B and/intersect C) = 0.01.

So, subbing these numbers in, you should get the correct answer!