If ` E and F `are the complementary events of events `E and F ,` respectively, and if P(F) `in` [0,1]

If barA and barB are the events complementary to the events A and B respectively, prove that, P(barA or barB)=1-P(A)P(B//A) .

If bar(A) and bar(B) are the events complementary to the events A and B respectively, prove that, P(bar(A) or bar(B)) = 1 - P(A cap B).

Define with examples : Complementary event.

If events A and B are complementary to each other, then P(B) =?

Prove that if E and F are independent events, then so are the events E and F'.

The maximum energies of photoelectrons emitted by a metal are E_(1) and E_(2) when the incident radiation has frequencies f_(1) and f_(2) respectively. Show that Planck's constant h and the work function W_(0) of the metal are h = (E_(1) - E_(2))/(f_(1) - f_(2)), W_(0) = (E_(1) f_(2) - E_(2) f_(1))/(f_(1) - f_(2))

If S be the sample space and E be the event then P(E)=

A die is thrown. If E is the event the number appearing is a multiple of 3' and F be the event 'the number appearing is even' then find whether E and F are independent ?

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ? (i) E : 'the card drawn is a spade F: 'the card drawn is an ace' (ii) E : 'the card drawn is black' F: 'the card drawn is a king' (iii) E: 'the card drawn is a king or queen' F: 'the card drawn is a queen or jack'.