सिद्ध कीजिए कि यदि `E_(1)" व "E_(2)` दो स्वतन्त्र घटनाएँ है तो `E_(1)" व E_(2)'` भी स्वतन्त्र होगी |

If E_(1) and E_(2) are two events such that P(E_(1)) = 0.5, P(E_(2)) = 0.3 and P(E_(1) and E_(2)) = 0.1 , find (i) P(E_(1) " or " E_(2)) (ii) P(E_(1) " but not " E_(2)) (iii) P(E_(2) " but not " E_(1)) (iv) P(" neither " E_(1) " nor " E_(2))

For any two independent events E_(1) and E_(2) in a space S , P [(E_(1) cup E_(2) ) cap (bar(E_(1)) cap bar(E )_(2))] is :

For two events E_(1) and E_(2), P(E_(1))=1/2,P(E_(2))=1/3 and P(E_(1)nnE_(2))=1/10 . Find: (i) P(E_(1) "or" E_(2)) (ii) P(E_(1) "but not" E_(2)) (iii) P(E_(2)"but not" E_(1)) (iv) P (neithter E_(1) not E_(2) )

= E_ (1), E_ (2), E_ (3), E_ (1), E_ (5) and P (E_ (1)) = (95) / (100), P (E_ (2) | E_ (1)) = (93) / (99), P (E_ (3) | E_ (1) E_ (2) E_ (3)) = (92) / (97) and P (E_ (5) | E_ (1) E_ (2) E_ (3) E_ (4)) = (91) / (96) n P (E) equals

If E_(1) and E_(2) are independent events such that P(E_(1))=0.3 and P(E_(2))=0.4 , find (i) P(E_(1) nn E_(2)) (ii) P(E_(1) uu E_(2)) (iii) P(bar(E_(1))nn bar(E_(2))) (iv) P(bar(E_(1)) nn E_(2)) .

Let E_(1) and E_(2) be the events such that P(E_(1))=1/3 and P(E_(2))=3/5 . Find : (i) P(E_(1)uuE_(2)) , where E_(1) and E_(2) are mutually ecclusive, (ii) P(E_(1) nn E_(2)) , when E_(1) and E_(2) are independent.

An urn contains four balls bearing numbers 1,2,3 and 123 respectively . A ball is drawn at random from the urn. Let E_(p) i = 1,2,3 donote the event that digit i appears on the ball drawn statement 1 : P(E_(1)capE_(2)) = P(E_(1) cap E_(3)) = P(E_(2) cap E_(3)) = (1)/(4) Statement 2 : P_(E_(1)) = P(E_(2)) = P(E_(3)) = (1)/(2)

An urn contains four balls bearing numbers 1,2,3 and 123 respectively . A ball is drawn at random from the urn. Let E_(p) i = 1,2,3 donote the event that digit i appears on the ball drawn statement 1 : P(E_(1)capE_(2)) = P(E_(1) cap E_(3)) = P(E_(2) cap E_(3)) = (1)/(4) Statement 2 : P_(E_(1)) = P(E_(2)) = P(E_(3)) = (1)/(2)

For any two independent events E_(1) and E_(2), P {(E_(1) cup E_(2)) cap (bar(E ) _(1) cap bar(E )_(2)) } is