# 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