A sample space consists of 9 elementary event `E_1, E_2, E_3 ..... E_8, E_9` whose probabilities are `P(E_1) = P(E_2) = 0. 08` ,`P(E_3) = P(E_4) = 0. 1`, `P(E_6) = P(E_7) = 0. 2` ,`P(E_8) = P(E_9) = 0. 07`. Suppose `A = {E_1,E_5,E_8}`, `B = {E_2, E_5, E_8, E_9}`. Compute `P(A)`, `P(B)` and `P(AnnB)`. Using the addition law of probability, find `P(AuuB)`. List the composition of the event `AuuB`, and calculate, `P(AuuB)` by adding the probabilities of the elementary events. Calculate `P(barB)` from `P(B)`, also calculate `P(barB)` directly from the elementary events of `barB`.

Explanation

Here, `P(E_1) = P(E_2) = 0.08`

`P(E_3) = P(E_4) = 0.1`

`P(E_6) = P(E_7) = 0.2`

`P(E_8) = P(E_9) = 0.07`

First we will calculate `P(E_5).`

As sample space contains events from `E_1` to `E_9.`

`:. P(E_1)+P(E_2)+P(E_3)+P(E_4)+P(E_5)+P(E_6)+P(E_7)+P(E_8)+P(E_9) = 1`

`=>0.08+0.08+0.1+0.1+P(E_5)+0.2+0.2+0.07+0.07 = 1`

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