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Let $E_1$ and $E_2$ be the two independent events.Such that $P(E_1)=p_1$ and $P(E_2)=p_2$.

Describe in words of the events whose probabilities are:\[(i)\;p_1p_2\quad(ii)\;(1-p_1)p-2\quad(iii)\;1-(1-p_1)(1-p_2)\quad(iv)\;p_1+p_2-2p_1p_2.\]

1 Answer

  • \(P(E_1)\)=\(P_1\) \(P(E_2)\)=\(P_2\)
  • \(E_1\)and\(E_2\) are indenpendent
  • \(P(E_1(\cap)E_2)\)=\(P(E_1)\) \(P(E_2)\)
  • \(P_1\)\(P_2\)\)=\(P(E_1)\) \(P(E_2)\)
  • =\(P(E_1(\cap)E_2)\)
  • =probability of simultanious occurance of\(E_1\)\(E_2\)
=probability of simultanious occurance of\(E_2\)and non occurance of\(E_1\)
=probability only occurance of\(E_2\)
1-(1-\(P_1\))(1-\(P_2\))=1-\(P(\bar{E}_1)\) \(P(\bar{E}_2)\)
=probability eather \(E_1\) or\(E_2\)occurance
\(P_1\)+\(P_2\)-2\(P_1\)\(P_2\)=\(P(E_1)\)+ \(P(E_2)\)-\(P(E_1(\cap)E_2)\)
probability exactly one of the event \(E_1\) or\(E_2\)occurance
answered Feb 25, 2013 by poojasapani_1

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