Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Melanie goes to a shelter to buy a dog. She has settled on two dogs, an Alsatian and a bulldog. To decide between them, she plans to flip a coin. Before she does, she flips the coin 50 times to check for fairness of the model. Her results are shown in the table.
Coin Toss Result Times Result Occurred
heads 24
tails 26
The relative frequency of landing on heads is $\square$ . The relative frequency of landing on tails is $\square$ .
Answer (2)
Calculate the relative frequency of heads: 50 24 = 0.48 .
Calculate the relative frequency of tails: 50 26 = 0.52 .
The relative frequency of heads is 0.48 .
The relative frequency of tails is 0.52 .
0.48 , 0.52
Explanation
Understand the problem Melanie flipped a coin 50 times to check its fairness. The coin landed on heads 24 times and on tails 26 times. We need to find the relative frequency of landing on heads and tails.
Define relative frequency The relative frequency of an event is the number of times the event occurs divided by the total number of trials. In this case, the number of trials is the total number of coin flips, which is 50.
Calculate relative frequency of heads To find the relative frequency of landing on heads, we divide the number of times the coin landed on heads (24) by the total number of flips (50): 50 24 = 0.48
Calculate relative frequency of tails To find the relative frequency of landing on tails, we divide the number of times the coin landed on tails (26) by the total number of flips (50): 50 26 = 0.52
State the final answer The relative frequency of landing on heads is 0.48, and the relative frequency of landing on tails is 0.52.
Examples
Relative frequency is used in many real-world scenarios, such as predicting weather patterns or analyzing the performance of a sports team. For example, if a basketball player has made 75 out of 100 free throws, their relative frequency of making a free throw is 75/100 = 0.75, or 75%. This can be used to estimate the probability of the player making their next free throw.
The relative frequency of landing on heads is 0.48, and the relative frequency of landing on tails is 0.52. This indicates that the coin is fairly balanced in outcomes based on the results Melanie obtained from her coin flips. Therefore, the calculations show no significant bias toward heads or tails.
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