Short Answer TypeA die is thrown and the sum of the numbers appearing is observed to be 7. What is the conditional probability that the number 2 has appeared at least once.
Let the events be
E : number 2 appears at least at least once
F : the sum of the numbers appearing is 7.
The elementary events favorable to the occurence of E are
(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2). (6, 2).
The elementary events favorable to the occurance of F are
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).
The elementary events favorable to the occurence of both E and F are (2, 5),(5. 2).
Find the probability that a single throw of a die results in a number less than 6 if
(i) no other information is given
(ii) it is given that the throw resulted in an odd number
A pair of dice is thrown . If the sum is seven, find the probability that one of the dice shows 3.
A die thrown three times,
E : 4 appears on the third toss,
F : 6 and 5 appears respectively on First two tosses
Determine P(E | F).
A coin is tossed three times, where
E : head on third toss, F : heads on first two tosses
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