1
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0 Let S be the sample space of all 3 $$\times$$ 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by

E1 = {A$$\in$$S : det A = 0} and

E2 = {A$$\in$$S : sum of entries of A is 7}.

If a matrix is chosen at random from S, then the conditional probability P(E1 | E2) equals ...............
2
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least $$0.96,$$ is
3
JEE Advanced 2013 Paper 1 Offline
Numerical
+4
-0
Of the three independent events $${E_1},{E_2}$$ and $${E_3},$$ the probability that only $${E_1}$$ occurs is $$\alpha ,$$ only $${E_2}$$ occurs is $$\beta$$ and only $${E_3}$$ occurs is $$\gamma .$$ Let the probability $$p$$ that none of events $${E_1},{E_2}$$ or $${E_3}$$ occurs satisfy the equations $$\left( {\alpha 2\beta } \right)p = \alpha \beta$$ and $$\left( {\beta - 3\gamma } \right)p = 2\beta \gamma .$$ All the given probabilities are assumed to lie in the interval $$(0, 1)$$.

Then $${{\Pr obability\,\,of\,\,occurrence\,\,of\,\,{E_1}} \over {\Pr obability\,\,of\,\,occurrence\,\,of\,\,{E_3}}}$$

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