Three coins are tossed. Events `E_1, E_2, E_3 and E_4` are defined as follows. `E_1`: Occurrence of at least two heads. `E_2`: Occurrence of at least two tails. `E_3` Occurrence of at most one head. `E_4`: Occurrence of two heads. Describe the sample space and events `E_1,E_2,E_3 and E_4`. Find `E_1uuE_4,E'_3`. Also check whether `E_2 and E_3` are equal.

Three coins are tossed. Events E_1, E_2, E_3 and E_4 are defined as follows. E_1 : Occurrence of at least two heads. E_2 : Occurrence of at least two tails. E_3 Occurrence of at most one head. E_4 : Occurrence of two heads. Describe the sample space and events E_1,E_2,E_3 and E_4 . Find E_1uuE_4,E'_3 . Also check whether E_1 and E_2 are mutually exclusive.

4 coins are tossed . Th e probability that they are all heads is

For any two independent events E_1 and E_2 P{(E_1uuE_2)nn(bar(E_1)nnbar(E_2)} is

If e_1 and e_2 are the eccentricities of a parabola and ellipse respectively, then:

The balancing lengths for the cells of emfs E_1 and E_2 are l_1 and l_2 respectively . If they are connected separately then

If E_1 and E_2 are equally likely, mutually exclusive and exhaustive events and P(A/E_1)=0.2, P(A/E_2)=0.3 , find P(E_1/A)

The Probability that at least one of the events E_(1) and E_(2) will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find P(barE_(1))+P(barE_(2))

Electric field on the axis of a small eletric dipole at a distance r is E_1 and at a distance of 2r on its perpendicular bisector, the electric field is E_2 . Then the ratio E_2:E_1 is

A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then P(E/F) is equal to:

If e_1 and e_2 be the eccentricities of two conjugate hyperbola, then 1/e_1^2+1/e_2^2 is :