Santos flipped a coin 300 times. The coin landed heads up 175 times. Find the ratio of heads to the total number of coin flips. Express as a simplified ratio.
A. 5 to 12
B. 7 to 5
C. 7 to 12
D. 12 to 7
Answer (1)
The problem requires finding the simplified ratio of heads to total coin flips.
Express the ratio as a fraction: 300 175 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 25: 300 ÷ 25 175 ÷ 25 = 12 7 .
The simplified ratio is 12 7 .
Explanation
Understand the problem We are given that Santos flipped a coin 300 times and it landed heads up 175 times. We need to find the ratio of heads to the total number of coin flips and express it in simplest form.
Define the ratio The ratio of heads to total flips is given by Total number of flips Number of heads .
Substitute the values We are given that the number of heads is 175 and the total number of flips is 300. Therefore, the ratio is 300 175 .
Find the GCD To simplify the ratio 300 175 , we need to find the greatest common divisor (GCD) of 175 and 300. From the tool, the GCD of 175 and 300 is 25.
Simplify the ratio Now, we divide both the numerator and the denominator by the GCD, which is 25. So, 300 175 = 300 ÷ 25 175 ÷ 25 = 12 7 .
State the final answer Therefore, the simplified ratio of heads to total number of coin flips is 12 7 , which can be expressed as 7 to 12.
Examples
In probability, ratios are often used to express the likelihood of an event occurring. For example, if you're analyzing the results of a series of experiments, the ratio of successful outcomes to total trials gives you an estimate of the probability of success. If a basketball player makes 7 out of every 12 free throws, this ratio (7 to 12) helps predict their future performance and can be used to make strategic decisions during a game.
