Question

Help!

The parallel circuit works if one connector works or both work.
Suppose that connectors work independently of each other and, further,
the probability of each component working is 0.84 and 0.72 respectively. What is the probability the parallel circuit works?

Answer 1

Connectors be C1 and C2

• P(C1)=0.84
• P(C2)=0.72

We need P(C1.C2)

Note the formula

For independent events

`\boxed{\sf P(AB)=P(A)P(B)}`

`\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)`

`\\ \tt{:}\dashrightarrow 0.84(0.72)`

`\\ \tt{:}\dashrightarrow 0.6`

Answer 2

• P(A)=0.84
• P(B)=0.72

Now A and B are independent

Both connectors must work together to make the parallel circuit work

P(A and B)

• P(A)*P(B)
• (0.84)(0.72)
• 0.6048