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Let E1 and E2 be two independent events such that \[p({{\mathbf{E}}_{\mathbf{1}}})\text{ }=~{{p}_{\mathbf{1}}}~\] and \[\mathbf{P}({{\mathbf{E}}_{\mathbf{2}}})\text{ }=\text{ }{{\mathbf{p}}_{\mathbf{2}}}\]. Describe in words of the events whose probabilities are: \[\left( \mathbf{i} \right)~{{p}_{\mathbf{1}}}~{{p}_{\mathbf{2}}}~\left( \mathbf{ii} \right)\text{ }(\mathbf{1}{{p}_{\mathbf{1}}})~{{p}_{\mathbf{2}}}~\left( \mathbf{iii} \right)\text{ }\mathbf{1}\text{ }\text{ }(\mathbf{1}\text{ }~{{p}_{\mathbf{1}}})(\mathbf{1}\text{ }~{{p}_{\mathbf{2}}})\text{ }\left( \mathbf{iv} \right)~{{p}_{\mathbf{1}}}~+~{{p}_{\mathbf{2}}}~\text{ }\mathbf{2}{{p}_{\mathbf{1}}}{{p}_{\mathbf{2}}}\]
Let E1 and E2 be two independent events such that \[p({{\mathbf{E}}_{\mathbf{1}}})\text{ }=~{{p}_{\mathbf{1}}}~\] and \[\mathbf{P}({{\mathbf{E}}_{\mathbf{2}}})\text{ }=\text{ }{{\mathbf{p}}_{\mathbf{2}}}\]. Describe in words of the events whose probabilities are: \[\left( \mathbf{i} \right)~{{p}_{\mathbf{1}}}~{{p}_{\mathbf{2}}}~\left( \mathbf{ii} \right)\text{ }(\mathbf{1}{{p}_{\mathbf{1}}})~{{p}_{\mathbf{2}}}~\left( \mathbf{iii} \right)\text{ }\mathbf{1}\text{ }\text{ }(\mathbf{1}\text{ }~{{p}_{\mathbf{1}}})(\mathbf{1}\text{ }~{{p}_{\mathbf{2}}})\text{ }\left( \mathbf{iv} \right)~{{p}_{\mathbf{1}}}~+~{{p}_{\mathbf{2}}}~\text{ }\mathbf{2}{{p}_{\mathbf{1}}}{{p}_{\mathbf{2}}}\]
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Probability
Let E1 and E2 be two independent events such that \[p({{\mathbf{E}}_{\mathbf{1}}})\text{ }=~{{p}_{\mathbf{1}}}~\] and \[\mathbf{P}({{\mathbf{E}}_{\mathbf{2}}})\text{ }=\text{ }{{\mathbf{p}}_{\mathbf{2}}}\]. Describe in words of the events whose probabilities are: \[\left( \mathbf{i} \right)~{{p}_{\mathbf{1}}}~{{p}_{\mathbf{2}}}~\left( \mathbf{ii} \right)\text{ }(\mathbf{1}{{p}_{\mathbf{1}}})~{{p}_{\mathbf{2}}}~\left( \mathbf{iii} \right)\text{ }\mathbf{1}\text{ }\text{ }(\mathbf{1}\text{ }~{{p}_{\mathbf{1}}})(\mathbf{1}\text{ }~{{p}_{\mathbf{2}}})\text{ }\left( \mathbf{iv} \right)~{{p}_{\mathbf{1}}}~+~{{p}_{\mathbf{2}}}~\text{ }\mathbf{2}{{p}_{\mathbf{1}}}{{p}_{\mathbf{2}}}\]

Here, \[p({{\mathbf{E}}_{\mathbf{1}}})\text{ }=~{{p}_{\mathbf{1}}}~\] and \[\mathbf{P}({{\mathbf{E}}_{\mathbf{2}}})\text{ }=\text{ }{{\mathbf{p}}_{\mathbf{2}}}\]

Now, its clearly seen that either \[{{E}_{1}}~or\text{ }{{E}_{2}}~\] occurs but not both.

i

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