There are 100 resistors in a box with the following characte

There are 100 resistors in a box with the following characteristics An experiment consists of selecting a resistor from the box at random. Define the following events: D = choose a 22 ohm resistor E = choose a 10% tolerance resistor F = choose a 5% tolerance resistor Find P(D), P{E), P(D E), P{D\\E), and P(E\\D). Define mutually-exclusive events B1 and B2 (i.e., B1 B2 = ) such that S = B1 B2- These two properties make {B1, B2} a partition of S. Use the total probability law to compute P(D) of part (a). (c) Use Bayes\' rule to find P(F\\D).

Solution

a)

From the table,

P(D) = 24/100 = 0.24
P(E) = 38/100 = 0.38
P(D n E) = 14/100 = 0.14
P(D|E) = 14/38 = 0.368421053
P(E|D) = 14/24 = 0.583333333

b)

We can set

B1 = with 5% tolerance
B2 = with 10% tolerance

P(D) = P(B1) P(D|B1) + P(B2) P(D|B2) = (0.62)(10/62) + (0.38)(14/38) = 0.24 [ANSWER]

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C)

P(F|D) = P(F n D)/P(D)

Thus, as by Bayes\' Rule,

P(F n D) = P(F) P(D|F) = 0.62(10/62) = 0.10

Therefore,

P(F|D) = P(F n D)/P(D) = 0.10/0.24 = 0.416666667 [answer]