Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • are events in a probability space satisfying the following constraints <img a

\mathrm{E_1 and E_2} are events in a probability space satisfying the following constraints \mathrm{P\left(E_1\right)=P\left(E_2\right) ; P\left(E_1 \cup E_2\right)=1 ; E_1 and\: E_2 } are independent

then \mathrm{P}\left(\mathrm{E}_1\right)=

Option: 1

0


Option: 2

\frac{1}{4}


Option: 3

\frac{1}{2}


Option: 4

1


Answers (1)

best_answer

Let \mathrm{ P\left(E_1\right)=P\left(E_2\right)=p } then using Addition theorem of probability

\mathrm{ P\left(E_1 \cup E_2\right)=P\left(E_1\right)+P\left(E_2\right)-P\left(E_1 \cap E_2\right) }

[ \because   in case of independent events ]

\mathrm{\begin{aligned} P\left(E_1 \cap E_2\right) & =P\left(E_1\right) P\left(E_2\right) \\ 1 & =+p-p^2 \end{aligned}}

\\or\: p^2-2 p+1=0\\ or\\ p=1

Posted by

mansi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question