MATH SOLVE

2 months ago

Q:
# Among 8846 cases of heart pacemaker malfunctions, 375 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 8846 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Accepted Solution

A:

Step-by-step explanation:Probability, P = [tex]\frac{no. of favourable outcomes}{Total no. of possible outcomes}[/tex]Out of 8846 heart pacemaker malfunctions cases, caused by firmware cases are 375then, no. of cases not caused by firmware are:8846 - 375 = 8471Probability for three different pacemakers respectively is given by:P(1) = [tex]\frac{8471}{8846}[/tex] we select the next malfunctioned pacemaker from the remaining i.e., out of 8471, excluding the chosen malfunctioned pacemakerP(2|1) = [tex]\frac{8470}{8845}[/tex] Therefore, the events are not independent of each other Now, if the selection is without replacement, thenP(3|1 & 2) = [tex]\frac{8469}{8844}[/tex]Now, by general multiplication rule(as the events are not independent):P(none of the 3 are caused by malfunction) = [tex]\frac{8471}{8846}\times\frac{8470}{8845}\times\frac{8469}{8844}[/tex]= 0.9019P(none of the 3 are caused by malfunction) = 90.19%The probability is high, therefore the whole batch will be accepted.