A house has a large window made of 15 equal-sized pieces of glass, each the same size and shape. There are 3 pieces of glass that are cracked. If a rock is thrown, what is the probability that the rock hits a piece of glass that is cracked?
A. [tex]$\frac{1}{12}$[/tex]
B. [tex]$\frac{1}{5}$[/tex]
C. [tex]$\frac{1}{4}$[/tex]
D. [tex]$\frac{1}{3}$[/tex]
Answer (2)
The problem gives 3 cracked pieces out of 15 total pieces.
The probability of hitting a cracked piece is the ratio of cracked pieces to total pieces.
Calculate the probability: 15 3 .
Simplify the fraction: 5 1 .
Explanation
Understand the problem We are given that a window has 15 equal-sized pieces of glass, and 3 of these pieces are cracked. A rock is thrown at the window, and we want to find the probability that the rock hits a cracked piece of glass.
Set up the probability The probability of hitting a cracked piece of glass is the ratio of the number of cracked pieces to the total number of pieces of glass.
Calculate the probability The probability is calculated as: Total number of pieces Number of cracked pieces = 15 3
Simplify the fraction We simplify the fraction 15 3 by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 15 ÷ 3 3 ÷ 3 = 5 1
State the final answer Therefore, the probability that the rock hits a cracked piece of glass is 5 1 .
Examples
Imagine you have a bag of marbles, some red and some blue. If you want to know the chance of picking a red marble, you would divide the number of red marbles by the total number of marbles. This is the same concept as finding the probability of the rock hitting a cracked piece of glass. For example, if you have a bag with 5 marbles and 1 is red, the probability of picking a red marble is 5 1 .
The probability that a rock hits a cracked piece of glass is 5 1 . This is calculated by dividing the number of cracked pieces (3) by the total pieces (15) and simplifying the fraction. Thus, the correct option is B. 5 1 .
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