Question

if a and b are two events such that p(a)=3/4 and p(b)=5/8,then find the minimum and maximum value of P(a U b)?




solve!! mods Dont delete the questions unnecessarily​

Answer 1

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

Given :-

• a and b are two events such that p(a)=3/4 and p(b)=5/8.

To Find :-

• Minimum and Maximum value of P(a U b).

Solution :-

MINIMUM :- The minimum of p(a U b) can be given considering that one of the given set of the subset of the other.

Means, here :

$\to \sf p(a) \subset \: p(b)$

And the union can be given as p(a) (as it has the maximum number of elements).

p(a) = 3/4 = 6/8

p(b) = 5/8

$\underline \frak{\therefore \:The \: minimum \: value \: of \: (a \: U \: b )= 3/4 }$

MAXIMUM : The minimum of p(a U b) can be given considering that both the sets are disjoint with no common elements. But if the sum crosses 1, one can be considered as the maximum value of (a U b).

Means, here :

$\to \sf\: p(a) + p(b) \: \: ({if \: less \: than \: 1}) \\ \: \to \sf1 \: \: ({if \: more \: than \: 1)}$

And the union can be given as 1 (as the sum exceeds 1).

p(a) + p(b) = 6/8 + 5/8

p(a) + p(b) = 11/8 (More than 1)

$\underline \frak{\therefore \:The \: maximum \: value \: of \: (a \: U \: b )= 1 }$

@SweetestBitter