A random variable X has probability distribution - X 1 2 3 4 5 6 7 8- PX 0-13 0-22 0-12 0-21 0-13 0-08 0-06 0-05- -If events are E-x is an odd number-F-x is divisible by 3 and G- x is less than 7 - then the value of PE- F- G is

The events are E={1,3,5,7} F={3,6} G={1,2,3,4,5,6} Now, F∩ G={3,6} E∪ F∩ G nbsp;={1,3,5,6,7} So, P{E∪{F∩ G }} =1 (0.22+0.21+0.05) =0.52 ...

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Standard XI

Mathematics

Probability Distribution

A random vari...

Question

A random variable $X$ has probability distribution

$\begin{matrix} X & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 P (X) & 0.13 & 0.22 & 0.12 & 0.21 & 0.13 & 0.08 & 0.06 & 0.05 \end{matrix}$

If events are $E = {x is an odd number},$ $F = {x is divisible by 3}$ and $G = {x is less than 7}$ , then the value of $P (E \cup (F \cap G))$ is

0.87

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0.77

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0.52

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0.82

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Solution

The correct option is C $0.52$
The events are
$E = {1, 3, 5, 7}$
$F = {3, 6}$
$G = {1, 2, 3, 4, 5, 6}$

Now,
$F \cap G = {3, 6} E \cup F \cap G = {1, 3, 5, 6, 7}$
So,
$P {E \cup {F \cap G}} = 1 - (0.22 + 0.21 + 0.05) = 0.52$

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A random variable X has probability distribution X12345678P(X)0.130.220.120.210.130.080.060.05 If events are E={x is an odd number},F={x is divisible by 3} and G={x is less than 7}, then the value of P(E∪(F∩G)) is

The correct option is C 0.52The events are E={1,3,5,7} F={3,6} G={1,2,3,4,5,6} Now, F∩G={3,6}E∪F∩G={1,3,5,6,7} So, P{E∪{F∩G}}=1−(0.22+0.21+0.05)=0.52

The correct option is C $0.52$
The events are
$E = {1, 3, 5, 7}$
$F = {3, 6}$
$G = {1, 2, 3, 4, 5, 6}$

Now,
$F \cap G = {3, 6} E \cup F \cap G = {1, 3, 5, 6, 7}$
So,
$P {E \cup {F \cap G}} = 1 - (0.22 + 0.21 + 0.05) = 0.52$