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:

No. of girls in the family | 2 | 1 | 0 |
---|---|---|---|

`No. of Families` | 32 | 154 | 14 |

`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}