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An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:
P (A fails) = 0.2
P (B fails alone) = 0.15
P (A and B fail) = 0.15
Evaluate the following probabilities:
(i) P (A fails | B has failed)
(ii) P (A fails alone)
(i) Let us assume the event which is failed by A is denoted by EA
And, event which is failed by B is denoted by EB
It is given in the question that,
Event failed by A, P (EA) = 0.2
Event failed by both,
And, event failed by B alone
0.15 = P (EB) – 0.15
∴ P (EB) = 0.30
Hence,
= 0.5
(ii) We have,
Probability where A fails alone
Suppose we have four boxes A, B, C and D containing coloured marbles as given below:
Box | Marble colour | ||
Red | White | Black | |
A | 1 | 6 | 3 |
B | 6 | 2 | 2 |
C | 8 | 1 | 1 |
D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?