Suppose you drop a die at random on the rectangular region shown in the figure above. What is the probability that it will land inside the circle with diameter 1m?
Suppose you drop a die at random on the rectangular region shown in the figure above. What is the probability that it will land inside the circle with diameter 1m?
The correct option is A π24
The die can land anywhere in the region−either in the circular zone or outside. Suppose the circular zone would have been covering(i.e. Area of Circle = Rectangular area) the whole rectangular area, then all the time the die would land one the circular area; the probability is maximum = 1. Similarly, if the circular zone(i.e Area of Circle<<Rectangular area) would have been very small such a that a die would hardly land on the same, the probability would have been impossible. Based on these, can we interpret that more than area of a circular are better the probability of a die would land on the circular zone. The question mentioned the area of circular zone is somewhat in between the above extreme condition. So the probability of a die could land would be evaluated based on the probability of circular zone within the rectangular zone. The circular area =π×(0.5)(0.5) =π4=P(Event) The Area of rectangular=3×2=6=P(Total). The probability that die would land on the circular area =P(Event)/P(Total)=π/24.
The die can land anywhere in the region−either in the circular zone or outside. Suppose the circular zone would have been covering(i.e. Area of Circle = Rectangular area) the whole rectangular area, then all the time the die would land one the circular area; the probability is maximum = 1. Similarly, if the circular zone(i.e Area of Circle<<Rectangular area) would have been very small such a that a die would hardly land on the same, the probability would have been impossible. Based on these, can we interpret that more than area of a circular are better the probability of a die would land on the circular zone. The question mentioned the area of circular zone is somewhat in between the above extreme condition. So the probability of a die could land would be evaluated based on the probability of circular zone within the rectangular zone. The circular area =π×(0.5)(0.5) =π4=P(Event) The Area of rectangular=3×2=6=P(Total). The probability that die would land on the circular area =P(Event)/P(Total)=π/24.
