# A Sample Space Consists of 9 Elementary Events E1, E2, E3, ..., E9 Whose Probabilities Are(Iv) Calculate P ( ¯ B ) from P(B), Also Calculate P ( ¯ B ) Directly from the Elementary Events of ¯ B . - Mathematics

A sample space consists of 9 elementary events E1E2E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1E5E8}, B = {E2E5E8, E9}

Calculate $P\left( \bar{ B} \right)$  from P(B), also calculate $P\left( \bar{ B } \right)$  directly from the elementary events of $\bar{ B }$ .

#### Solution

Let S be the sample space of the elementary events.
S = {E1E2E3, ..., E9}
Given:
A = {E1E5E8}
B = {E2E5E8, E9}
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07

$P\left( B \right) = 1 - P\left( B \right) = 1 - 0 . 32 = 0 . 68$  [From (i)]
Also, we know that  $\bar{ B }$= − B = {E1E3E4E6, E7}

∴ $P\left( \bar{B} \right)$ = P(E1) + P(E3) + P(E4) + P(E6) + P(E7)

= 0.08 + 0.1 + 0.1 + 0.2 + 0.2

= 0.68

#### Notes

The solution of the problem is provided by taking P(E5) = 0.1. This information is missing in the question as given in the book.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.4 | Q 28.4 | Page 69