Question

Given two independent events \(A\) and \(B\) such that \(P(A)=0.3,P(B)=0.6.\) Find:
(A)\(P(A\, and\, B)\)
(B)\(P(A\, and\, not\, B)\)
(C)\(P(A or B)\)
(D)\(P(neither\, A\, nor\, B)\)

Answer 1

It is given that \(P(A)=0.3,\)\(P(B)=0.6\)
\(A\) and \(B\) are independent events.

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(i)\(P(A\, and\, B)=P(A).P(B)\)
\(\implies P(A\cap B)=0.3\times 0.6\)
\(=0.18\)

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(ii)\(P\)(\(A\) and not \(B\))\(=P(A∩B')\)
\(=P(A)–P(A∩B)\)
\(=0.3–0.18\)
\(=0.12\)

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(iii)\(P\)(\(A\) or \(B\))
\(=P(A)+P(B)–P\)(\(A\) and \(B\))
\(=0.3+0.6–0.18\)
\(=0.9–0.18\)
\(=0.72\)

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(iv)\(P\)(neither \(A\) nor \(B\))=\(P(A'\cap B')\)
\(=1–P(A∪B)\)
\(=1–0.72\)
\(=0.28\)