The Event which is likely to occur, measured by the ratio of the Favourable cases to the whole number of cases possible , known as Probability.
Probability is a measure of the likelihood of an event occurring, which is determined by the ratio of favorable outcomes to the total number of possible outcomes.
The formula for calculating probability is:
Example 1: A Speak truth truth in 20 % of cases and B in 40 % of cases. In what Percentages of cases are they likely to Contradict to each other in Narrating the Same Event?
(a) 40 %
(b) 44 %
(c) 42 %
(d) None of these
Ans: (b)
They contradict each other if one of them Speaks and the other one lies. and vice – versa.
Required Percentages = 0.20 x (1 – 0.40 ) + (1 0.20) x 0.40 = 0.44 = 44 %.
Example 2: Two dice are rolled, find the probability that the sum is
(a) equal to 1
(b) equal to 4
(c) less than 13
Ans: (a)
The sample space S of two dice is shown below.
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
a) Let E be the event “sum equal to 1”. There are no outcomes which correspond to a sum equal to 1, hence
Quickest Way: Sum is always greater than or equal to 1 . So it is Impossible Event means Probability will be 0.
b) Three possible outcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.
c) All possible outcomes, E = S, give a sum less than 13, hence.
Quickest Way: Sum is always less than 13. So it is sure Event means Probability will be 1.
Example 3: Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tails).
(a) 1/4
(b) 1/2
(c) 3/2
(d) None of these
Ans: (a)
The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event “two heads are obtained”.
E = {(H,H)}
We use the formula of the classical probability.
Example 4: A die is rolled, find the probability that an even number is obtained?
(a) 3/4
(b) 1/2
(c) 1/4
(d) None of these
Ans: (b)
Let us first write the sample space, S of the experiment.
S = {1,2,3,4,5,6}
Let E be the event “an even number is obtained” and write down.
E = {2,4,6}
We can use the formula of the classical probability.
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