| Study Case : Q. 21 to 25 |
| A man is sitting on a helicopter which is positioned in such a way that the entire garden is visible to him. The garden is rectangular in shape with a pond of diameter 2 m as shown in the figure. There is a semi-circular concrete patio at one end and two flower beds at the other two comers as shown. The remaining area has beautiful lush green grass. The man drops a ball from the helicopter. |
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| Based on the above information, answer the follows questions: |
A) \[\frac{11}{140}\]
B) \[\frac{11}{280}\]
C) 0
D) 1
Correct Answer: B
Solution :
| We know the probability of the occurrence of an event E is given by: |
| \[P(E)=\frac{\text{Number of outcomes favourable to E}}{\text{Total number of possible outcomes}}\] |
| \[\therefore \] The probability that the ball dropped will fall in one of the flower beds |
| \[=\frac{\text{Area of two flower beds}}{\text{Total area of garden}}\] |
| Here, total area of the garden \[=8\times 5=40{{m}^{2}}.\] |
| And, area of two flower beds \[=2\times \frac{1}{4}\times \pi {{r}^{2}}\] |
| \[=\frac{1}{2}\times \frac{22}{7}\times {{1}^{2}}=\frac{11}{7}{{m}^{2}},\] |
| as each flower bed is shaped like a quadrant of a circle of radius is 1 m. |
| \[\therefore \] Required probability \[=\frac{11/7}{40}=\frac{11}{280}\] |
| So, Option [b] is correct |
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