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boxford69
16.08.2020 •
Mathematics
There are three motors available to repair Ralph’s vacuum cleaner. Motor #1 has a 65% chance of breaking by the end of the week. Motor #2 has a 35% chance of breaking by the end of the week. Motor #3 has a 5% chance of breaking by the end of week. Suppose that Ralph randomly chooses one of the three motors so that each is equally likely, and then the motor does break by the end of the week. What is the conditional probability that Ralph installed motor #1?
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Ответ:
0.619
Step-by-step explanation:
from the question we have the following data:
probability of motor 1 breaking = 65% = 0.65
probability of motor 2 breaking = 35% = 0.35
probability of motor 3 breaking = 5% = 0.05
since we have 3 motors the probability of any of them breaking down is =![\frac{1}{3}](/tpl/images/0722/8969/5506e.png)
but what the question requires from us is the conditional probability of the first one being installed
we have to solve this questions using bayes theorem
such that:
=![\frac{0.2167}{0.2167+0.1167+0.0167}](/tpl/images/0722/8969/83218.png)
=![\frac{0.2167}{0.3501}](/tpl/images/0722/8969/7e148.png)
= 0.618966
approximately 0.619
therefore the conditional probability ralph installed the first motor is 0.619
Ответ:
£300 x 0.5 = £150
£150 x 6 = £900
£900 + £300 = £1200