# CBSE Class 10-Mathematics: Chapter – 15 Probability Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 12**:

A number is chosen at random from the numbers What is the probability that

**Answer**:

can take values

To set

Probability

**Question 12**:

A number is selected from the number and then a second number is randomly selected from the numbers . What is the probability that the product of the two numbers will be less than ?

**Answer**:

Number can be selected in three wavs and corresponding to each such wav there are three wavs of selecting number y. Therefore. Two numbers can be selected in wavs as listed below:

Favourable number of elementary events

Hence, required probability

**Question 14**:

In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region.

**Answer**:

We have

Using Pythagoras Theorem is A ABC. We have

Area of the circle

Area of shaded region circle – Area of rectangle ABCD

Area of shaded reeion .

Hence

**Question 15**:

In the fig points A. B. C and D are the centres of four circles. each having a radius of 1 unit. If a point is chosen at random from the interior of a square ABCD. What is the probability that the point will be chosen from the shaded region.

**Answer**:

Radius of the circle is 1 unit

Area of the circle = Area of a sector

Side of the square ABCD

Area of square

Area shaded region is

Area of square Area of sectors

Probability

**Question 16**:

In the adjoining figure ABCD is a square with sides of length units points are the mid points of the sides BC & CD respectively. If a point is selected at random from the interior of the square what is the probability that the point will be chosen from the interior of the square what is the probability that the point will be chosen from the interior of the triangles APO.

**Answer**:

Area of triangle

Area of triangle

Area of triangle ADQ

Area of triangle APO = Area of a square – (Area of a triangle PQC + Area of triangle ABP = Area of triangle ABP)

Probability that the point will be chosen from the interior of the triangle APO