Tips And Tricks And Shortcuts For Probability Questions

Question 3. Two dice are rolled, find the probability that the sum is

a) equal to 1 

b) equal to 4 

c) less than 13

Solution      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

P(E) = \frac{n(E)}{n(S)} = \frac{0}{36} = 0 

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.

P(E) = \frac{n(E)}{n(S)} = \frac{3}{36} = \frac{1}{12}

c) All possible outcomes, E = S, give a sum less than 13, hence.

P(E) = \frac{n(E)}{n(S)} = \frac{36}{36} = 1

Quickest Way : Sum is always less than 13 . So it is sure Event means Probability will be 1.

Question 4. 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?

                     Options

                    (a) 40 %

                    (b) 44 %

                    (c) 42 %

                    (d) None of these

Solutions    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 %

                     Correct Option (b)