P(A or B) = P(A) + P(B) - P(A) * P(B | A)
0.72 = P(A) + 0.45 - P(A) * 0.4
0.72 - 0.45 = P(A) - P(A) * 0.4
0.27 = P(A) * (1 - 0.4)
0.27 = P(A) * 0.6
P(A) = 0.27 / 0.6 = 0.45
The required probability is [tex]P(A)=0.45[/tex].
It is given that,
To find the value of [tex]P(A)=?[/tex].
We know that
[tex]P(A\text{ or }B)=P(A)+P(B)-P(A)P(B|A)[/tex]
Using the above formula, we get
[tex]0.72=P(A)+0.45-P(A)(0.4)[/tex]
[tex]0.72-0.45=P(A)(1-0.4)[/tex]
[tex]0.27=P(A)(0.6)[/tex]
[tex]\dfrac{0.27}{0.6}=P(A)[/tex]
[tex]0.45=P(A)[/tex]
Therefore, the required probability is [tex]P(A)=0.45[/tex].
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