Answer:
a) 0.04
b) 0.19
c) 0.01
d) 0.8
Step-by-step explanation:
Hi,
Let's make our data, considering two rules of probability:
- The total probability of any event is 1.
- Percentages are converted to decimal.
- P(M) = 0.95
- P(M')=0.05
- P(B)=0.80
- P(B')=0.20
- where M → Main Engine works, B → Back Up Engine works, M' → Main Engine will not work and B' → Back Up Engine will not work.
<em>Remember for cases with </em><em>and, </em><em>we multiply; for cases with </em><em>or</em><em>, we use addition.</em>
<em />
a) For this part, we know that Main Engine will work and Back-up engine will not work:
P(M' and B): 0.05 x 0.80 = 0.04
b) Back up will not work and Main will work:
P(M and B') = 0.20 x 0.95 = 0.19
c) We know the probability of entire component working, which is 0.99.
So to find the probability of entire component failing, we need to subtract 0.99 from 1. <em>(Since the total probability is always 1)</em>
P(Entire component will fail) = 1 - 0.99 = 0.01
d) This is a typical case of conditional probability, to calculate a conditional probability we use the following formula:
Where, means the probability of A, given B.
Simply using this, we calculate the :
<em>(as calculated in part a)</em>
<em /><em> (as calculated for the data)</em>
<em />
Modifying the formula to our needs:<em> </em><em />
⇒ Ans.
I hope this answers all your queries.