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# In a random experiment, let A and B be events such that P

Question:

In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and $P(\bar{A})$ = 0.4. Find P(B).

Solution:

Given : $\mathrm{P}\left({ }^{\bar{A}}\right)=0.4, \mathrm{P}(\mathrm{A}$ or $\mathrm{B})=0.7$ and $\mathrm{P}(\mathrm{A}$ and $\mathrm{B})=0.3$

To find : P(B)

Formula used : $\mathrm{P}(\mathrm{A})=1-\mathrm{P}(\bar{A})$

P(A or B) = P(A) + P(B) - P(A and B)

We have $\mathrm{P}(\bar{A})=0.4$

$P(A)=1-0.4=0.6$

We get $P(A)=0.6$

Substituting in the above formula we get,

$0.7=0.6+P(B)-0.3$

$0.7=0.3+P(B)$

$0.7-0.3=P(B)$

$0.4=P(B)$

P(B) = 0.4