40. Games To win a prize at a carnival game, you must toss a quarter, so that it lands entirely within a circle as shown at the right. Assume that the center of a tossed quarter is equally likely to land at any point within the 8-in. square.
a. What is the probability that the quarter lands entirely in the circle in
one toss?
b. Reasoning On average, how many coins must you toss to win a
prize? Explain.

a) 0.0139

b) 73

Step-by-step explanation:

a) The circle has a radius of 1 inch.  For the quarter to land entirely within the circle, the center of the quarter must lie within a circle with radius 17/32 inches.

The probability is the ratio of the area of this circle to the area of the square.

P = πr² / s²

P = π (17/32)² / (8)²

P ≈ 0.0139

b) Expected value = probability × frequency

1 = 0.0139 × n

n = 72.2

Rounding up to the nearest integer, you would expect to toss on average 73 quarters before getting one in the circle.

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632