select the correct answer.\nin a factory, the chance that a certain machine works without overheating in the…

select the correct answer.\nin a factory, the chance that a certain machine works without overheating in the morning is 50%. if it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. what is the probability that on a given day it will work in the morning and overheat later on?\na. 4%\nb. 3.75%\nc. 7.5%\nd. 3.5%

select the correct answer.\nin a factory, the chance that a certain machine works without overheating in the morning is 50%. if it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. what is the probability that on a given day it will work in the morning and overheat later on?\na. 4%\nb. 3.75%\nc. 7.5%\nd. 3.5%

Answer

Explanation:

Step1: Identify relevant probabilities

Let $P(\text{work in morning}) = 0.5$. The probability of over - heating later given it works in the morning is $P(\text{overheat later}|\text{work in morning})=0.15$.

Step2: Use conditional probability formula

The probability of two independent events $A$ and $B$ (here $A$ is working in the morning and $B$ is over - heating later) is $P(A\cap B)=P(A)\times P(B|A)$. So $P(\text{work in morning and overheat later})=P(\text{work in morning})\times P(\text{overheat later}|\text{work in morning})$. Substitute the values: $0.5\times0.15 = 0.075$.

Answer:

C. 7.5%