independent and dependent events

Question

In a carnival game called Spot the Spot, the player has to drop five disks onto a red circle. The disks must cover it completely for the player to win.   

The probability that a skilled player can drop one of the disks onto the exact place on the red circle that it must occupy is about 1/3. What is the probability that such a player will be able to drop

Answer 1

Hi Emma G.,

As noted above, the question is a poorly-geometrically-motivated setup. But let's assume that what is meant is, each disc the player drops has 1/3 probability of landing on the red disc, and that at least 3 discs must land on it. Then you have (1/3)^3 *(2/3)^2 *10 (probability that exactly three land correctly, and the ways of choosing those 3) + (1/3)^4 *(2/3)^1 *5 (probability that exactly 4 land correctly, and ways of choosing those 4) + (1/3)^5 = 51/243 .

A related, but more interesting problem, might be: a student can catch an object falling within 3 feet of their position (defined as a point). How many students would it require to assure that no dropped object hits the floor, in a square gym of size 30 feet x 30 feet? (Students are positioned in advance, and can't move around!)

-- Cheers, --Mr. d.