Katie flipped a coin 10 times. Her results are shown below.
| Outcome | Frequency |
|---|---|
| Heads | 3 |
| Tails | 7 |
a) Work out the experimental probability of the outcome being heads. Give your answer as a decimal.
Answer (2)
Calculate the experimental probability of heads by dividing the number of heads by the total number of flips.
The number of heads is 3, and the total number of flips is 10.
Calculate the probability: P ( He a d s ) = 10 3 .
Convert the fraction to a decimal: 0.3 .
Explanation
Understand the problem We are given the results of Katie flipping a coin 10 times. We need to find the experimental probability of getting heads. The experimental probability is the ratio of the number of times an event occurs to the total number of trials.
Calculate the probability The number of heads is 3, and the total number of flips is 10 (3 heads + 7 tails). Therefore, the experimental probability of getting heads is the number of heads divided by the total number of flips.
Express as a decimal The experimental probability of heads is calculated as: P ( He a d s ) = Total Number of Flips Number of Heads = 10 3 To express this probability as a decimal, we divide 3 by 10.
State the final answer Dividing 3 by 10, we get: 10 3 = 0.3 So, the experimental probability of the outcome being heads is 0.3.
Examples
Experimental probability is useful in many real-life situations. For example, if you wanted to know the probability of a basketball player making a free throw, you could record the number of free throws they make out of a certain number of attempts. If a basketball player makes 75 free throws out of 100 attempts, the experimental probability of them making a free throw is 100 75 = 0.75 . This can help predict their performance in future games. Similarly, in manufacturing, experimental probability can be used to estimate the likelihood of a product being defective based on the number of defective products found in a sample.
The experimental probability of getting heads in Katie's coin flips is calculated by dividing the number of heads (3) by the total flips (10), resulting in a probability of 0.3. This means there's a 30% chance of flipping heads based on the experiment. Therefore, the answer is 0.3.
;
