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Consider a circular target board with radius 10 inches. The target board is divided into 10 concentric circles, 1 inch wide, numbered 1 (outermost circle) to 10 (at center). A dart player is throwing darts at the target- blindfolded, until a dart sticks to the board. Assuming that the dart lands on any part of the board with equal probability and number the first dart hits is the random variable X: calculate - (a) Pr (X= 10) - hint: area of circles (b) Pr ( X = 6) (c) Pr (X=2) (d) Pr (X> 2)

Consider a circular target board with radius 10 inches. The target board is divided into 10 concentric circles, 1 inch wide, numbered 1 (outermost circle) to 10 (at center). A dart player is throwing darts at the target- blindfolded, until a dart sticks to the board. Assuming that the dart lands on any part of the board with equal probability and number the first dart hits is the random variable X: calculate - (a) Pr (X= 10) - hint: area of circles (b) Pr ( X = 6) (c) Pr (X=2) (d) Pr (X> 2)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem Overview: Dartboard Probability Analysis** Consider a circular target board with a radius of 10 inches. The target board is divided into 10 concentric circles, each 1 inch wide, numbered from 1 (outermost circle) to 10 (center). A dart player, who is blindfolded, throws darts at the target until a dart sticks to the board. Assume that the dart lands on any part of the board with equal probability. Let the number of the first circle hit by the dart be the random variable \( X \). Calculate the following probabilities: 1. \( \text{Pr}(X = 10) \) – hint: use the area of circles. 2. \( \text{Pr}(X = 6) \) 3. \( \text{Pr}(X = 2) \) 4. \( \text{Pr}(X > 2) \) **Note:** To solve these problems, consider the incremental area of each circle, as probability is proportional to the area of each concentric ring compared to the entire board.
Transcribed Image Text:**Problem Overview: Dartboard Probability Analysis** Consider a circular target board with a radius of 10 inches. The target board is divided into 10 concentric circles, each 1 inch wide, numbered from 1 (outermost circle) to 10 (center). A dart player, who is blindfolded, throws darts at the target until a dart sticks to the board. Assume that the dart lands on any part of the board with equal probability. Let the number of the first circle hit by the dart be the random variable \( X \). Calculate the following probabilities: 1. \( \text{Pr}(X = 10) \) – hint: use the area of circles. 2. \( \text{Pr}(X = 6) \) 3. \( \text{Pr}(X = 2) \) 4. \( \text{Pr}(X > 2) \) **Note:** To solve these problems, consider the incremental area of each circle, as probability is proportional to the area of each concentric ring compared to the entire board.
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