Question

in 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? select the correct answer. a. 4% b. 3.75% c. 7.5% d. 3.5%

Explanation:

Step1: Identify the probabilities

The probability that the machine works without over - heating in the morning is $P(M) = 50\%=0.5$. The probability that it stops due to over - heating in the afternoon given it worked in the morning is $P(A|M)=15\% = 0.15$.

Step2: Use the multiplication rule for conditional probability

The multiplication rule for conditional probability is $P(M\cap A)=P(A|M)\times P(M)$.
Substitute the values: $P(M\cap A)=0.15\times0.5$.
$P(M\cap A)=0.075 = 7.5\%$.

Answer:

C. 7.5%