Sets & Probability

Solved basic word problems on sets:

1. Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).

Solution: 

Using the formula n(A ∪ B) = n(A) + n(B) – n(A ∩ B). 

then n(A ∩ B) = n(A) + n(B) – n(A ∪ B) 

                     = 20 + 28 – 36 

                     = 48 – 36 

                     = 12 

2. If n(A – B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B).

Solution: 

Using the formula n(A∪B) = n(A – B) + n(A ∩ B) + n(B – A) 

                                 70 = 18 + 25 + n(B – A) 

                                 70 = 43 + n(B – A) 

                         n(B – A) = 70 – 43 

                         n(B – A) = 27 

Now n(B) = n(A ∩ B) + n(B – A) 

               = 25 + 27 

               = 52 

Probality

2. A survey of 200families shows the results given below:

Out of these families, one is chosen at random. What is the probability that the chosen family has 1 girl?

Solution:

Total number of families = 200.

Number of families having 1 girl = 154.Probability of getting a family having 1 girl

                               = ^{Number of families having 1 girl}/_{Total number of families}

                               = ¹⁵⁴/₂₀₀

                         = 77/100

A dice is thrown 65 times and 4 appeared 21 times. Now, in a random throw of a dice, what is the probability of getting a 4?

Solution:

Total number of tria1s = 65.

Number of times 4 appeared = 21.Probability of getting a 4 = Number of times 4 appeared/Total number of trials

                                  = ²¹/₆₅