(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Electric circuit (as shown in the picture), is made from five elements. Failures of elements are independent, with probabilites: [tex]A_1-0.6[/tex], [tex]B_1-0.4[/tex], [tex]B_2-0.7[/tex], [tex]B_3-0.9[/tex] and [tex]A_2-0.5[/tex]. Find the probabilty of current break, between [tex]M[/tex] and [tex]N[/tex].

2. Relevant equations

For independent events:

[tex]P(A\cap B] = P(A)\cdot P(B)[/tex]

[tex]P(A\cup B] = P(A) + P(B) - P(A)\cdot P(B)[/tex]

3. The attempt at a solution

Current will be break, when any of the [tex]A[/tex] element fail, or if all of the [tex]B[/tex] elements fail. So probabilty of the current break is: [tex]A_1 \cap\left[B_1\cup B_2\cup B_3\right]\cap A_2[/tex].

So:

[tex]B = B_1\cup B_2\cup B_3 = B_1\cdot B_2\cdot B_3[/tex]

And, finaly, probability is:

[tex]A_1 \cap\left[B_1\cup B_2\cup B_3\right]\cap A_2 = A_1 \cap B\cap A_2 = A_1 + A_2 + B - A_1\cdot B - A_1\cdot A_2 - A_2\cdot B + A_1\cdot A_2 \cdot B[/tex].

Is that correct ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Probability (electric circuit) - need confirmation of my solution

**Physics Forums | Science Articles, Homework Help, Discussion**