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Maths-

General

Easy

Question

If $P space open parentheses A union B close parentheses equals 3 over 4$ and $P space open parentheses A with ‾ on top close parentheses equals 2 over 3$ , then $P space open parentheses A with ‾ on top intersection B close parentheses equals$

5/12
7/12
$\frac{1}{12}$
1/2

hint Hint:

$A with ‾ on top intersection B space a n d space A space a r e space m u t u a l l y space e x c l u s i v e space e v e n t s$ .

The correct answer is: 5/12

$S i n c e space space space space A with ‾ on top intersection B space a n d space A space a r e space m u t u a l l y space e x c l u s i v e space e v e n t s$ .
$P left parenthesis A right parenthesis space equals space 1 minus space P space open parentheses A with ‾ on top close parentheses$
$P left parenthesis A right parenthesis space equals space 1 space minus space 2 over 3 space equals space 1 third$
$left square bracket space P space open parentheses A with ‾ on top intersection B close parentheses space equals space P left parenthesis B right parenthesis space equals space P left parenthesis space A intersection B right parenthesis space right square bracket space...... space left parenthesis 1 right parenthesis$
Also, we know that
$P left parenthesis A union B right parenthesis space equals space P left parenthesis A right parenthesis space plus space P left parenthesis B right parenthesis space minus P left parenthesis A intersection B right parenthesis$
From (1)
$P left parenthesis A union B right parenthesis space equals space P left parenthesis A right parenthesis space plus space P space open parentheses A with ‾ on top intersection B close parentheses$
$P left parenthesis A union B right parenthesis space equals space 1 third space plus space P space open parentheses A with ‾ on top intersection B close parentheses$
$P space open parentheses A with ‾ on top intersection B close parentheses space equals space 3 over 4 minus space 1 third space equals space 5 over 12$

Related Questions to study

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If $P space open parentheses A close parentheses equals 0.4 comma P space open parentheses B close parentheses equals 0.5 comma P space open parentheses C close parentheses equals 0.6$ $P space open parentheses A intersection B close parentheses equals 0.2 comma P space open parentheses B intersection C close parentheses equals 0.3 comma P space open parentheses C intersection A close parentheses equals 0.25$ $P space open parentheses A intersection B intersection C close parentheses equals 0.1$ then $P space open parentheses A union B union C close parentheses equals$

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