A circular target of radius 11 cm is to be hit as a game. The dart board has three concentric circles inside the bigger board of radii 7, 9 and 10 cm respectively,dividing the board into four regions.If Sarthak shot the dart 121 times, find the probability of the dart hitting each region.

To find the probability of the dart hitting each region, we need to determine the areas of the different regions on the dart board.

Let's start by calculating the area of the whole dart board. Since it is a circle with a radius of 11 cm, we can use the formula for the area of a circle: A = πr^2.

Area of the whole dart board = π * (11 cm)^2

Next, we calculate the areas of the concentric circles inside the dart board.

The area of a circle with radius 7 cm = π * (7 cm)^2
The area of a circle with radius 9 cm = π * (9 cm)^2
The area of a circle with radius 10 cm = π * (10 cm)^2

Now, we can calculate the areas of the different regions on the dart board.

Region 1: This is the area between the circle with radius 7 cm and the circle with radius 9 cm. To find the area, we subtract the area of the smaller circle from the area of the larger circle.

Area of Region 1 = (π * (9 cm)^2) - (π * (7 cm)^2)

Region 2: This is the area between the circle with radius 9 cm and the circle with radius 10 cm. Again, we subtract the area of the smaller circle from the area of the larger circle.

Area of Region 2 = (π * (10 cm)^2) - (π * (9 cm)^2)

Region 3: This is the area between the circle with radius 10 cm and the outer circle with radius 11 cm. We subtract the area of the smaller circle from the area of the larger circle.

Area of Region 3 = (π * (11 cm)^2) - (π * (10 cm)^2)

Region 4: This is the area outside the outer circle with radius 11 cm.

Area of Region 4 = Area of the whole dart board - (Area of Region 1 + Area of Region 2 + Area of Region 3)

Now that we have calculated the areas of the different regions, we can find the probability of the dart hitting each region.

Probability of hitting Region 1 = (Area of Region 1) / (Area of the whole dart board)
Probability of hitting Region 2 = (Area of Region 2) / (Area of the whole dart board)
Probability of hitting Region 3 = (Area of Region 3) / (Area of the whole dart board)
Probability of hitting Region 4 = (Area of Region 4) / (Area of the whole dart board)

Just substitute the calculated areas into the formulas to find the probabilities for each region.