Short Answer Type
Long Answer TypeHere 
Number of elements (outcomes) of the above sample space is 6 × 6 = 36.
Let E : the sum of numbers on the dice is 4
∴ E = {(1, 3), (2, 2), (3, 1)}
and F : numbers appearing on the two dice are different
∴ F contains all the points of S except (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6).
∴ F contains 30 elements.
Also E ∩ F = {(1, 3), (3, 1)}
Required probability = 
Short Answer TypeTwo coins are tossed once, where
E : tail appears on one coin, F : one coin shows head
Determine P(E | F).
Two coins are tossed once, where
E : no tail appears, F : no head appears
Determine P(E | F).
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