Question

The probability of two machines each independently working successfully are 0.8 and 0.9. What is the probability of only one machine operating successfully at a time?

A) 0.18
B) 0.26
C) 0.72
D) 0.92

Answer 1

To find the probability of only one machine operating successfully out of two with independent probabilities, we sum the probabilities of each individual scenario where only one machine works. The calculation leads to a probability of 0.26, so the correct answer is B) 0.26.

Step-by-step explanation:

The question is asking for the probability of only one machine operating successfully when two machines each have independent probabilities of working successfully. The two machines have probabilities of 0.8 and 0.9 respectively.

There are two scenarios for only one machine working:

• Machine 1 works (with a probability of 0.8) and Machine 2 does not work (with a probability of 0.1).
• Machine 2 works (with a probability of 0.9) and Machine 1 does not work (with a probability of 0.2).

We calculate the probability of each scenario and then sum them to get the probability of only one machine working at a time:

P(Only Machine 1 works) = 0.8 * 0.1 = 0.08

P(Only Machine 2 works) = 0.2 * 0.9 = 0.18

Therefore, the probability of only one machine working at a time is:

P(Only one machine works) = P(Only Machine 1 works) + P(Only Machine 2 works) = 0.08 + 0.18 = 0.26

The correct answer is B) 0.26.