A basket of fruits contains 5 apples and 3 pears. Sharon took two fruits at random. What is the probability that both fruits are apples? Write your answer in the simplest form of fraction.(1 point)
A coin is flipped and a spinner is spun simultaneously. The spinner is divided into six equally sized sections labeled with 1, 2, 3, 4, 5, 6. What is the probability of flipping a tail and landing on 5?(1 point)
There are a total of 8 fruits in the basket. If Sharon takes two fruits at random, the probability that the first fruit she takes is an apple is 5/8. Since she does not replace the fruit back in the basket, there are now only 4 apples left out of a total of 7 fruits. Therefore, the probability that the second fruit she takes is also an apple is 4/7.
To find the probability that both fruits are apples, we need to multiply the probabilities of each event:
5/8 x 4/7 = 20/56 = 5/14
Therefore, the probability that both fruits are apples is 5/14.
Well, let's analyze the situation.
First, we know that there are a total of 8 fruits in the basket: 5 apples and 3 pears.
So, when Sharon takes the first fruit, there are 8 options for her. However, if she takes an apple, there would be 4 apples left in the basket (since there were a total of 5 apples originally).
Now, if she takes a second fruit without replacement, there would be only 7 fruits left in the basket. And since there would now be 4 apples left, the probability of her picking an apple again would be 4 out of 7.
So, the probability of Sharon picking two apples in a row can be calculated as:
(5/8) * (4/7) = 20/56 = 5/14
Therefore, the probability that Sharon takes two apples is 5/14.
To find the probability of both fruits being apples, we need to calculate the ratio of the number of favorable outcomes (2 apples) to the total number of possible outcomes (8 fruits in total).
The probability can be calculated as follows:
Number of favorable outcomes = Number of ways to select 2 apples from 5 = C(5, 2) = 5! / (2! * (5 - 2)!) = (5 * 4) / (2 * 1) = 10
Total number of possible outcomes = Number of ways to select 2 fruits from 8 = C(8, 2) = 8! / (2! * (8 - 2)!) = (8 * 7) / (2 * 1) = 28
Therefore, the probability that both fruits are apples is 10/28.
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
10 ÷ 2 / 28 ÷ 2 = 5/14
So, the probability that both fruits are apples is 5/14.
To find the probability that both fruits are apples, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes when Sharon takes two fruits at random. The total number of fruits in the basket is 5 apples + 3 pears = 8 fruits.
Now, let's find the number of favorable outcomes, which is the number of ways Sharon can choose 2 apples out of 5 apples. We can calculate this using combinatorics. The formula for calculating combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen.
In this case, we want to calculate 5C2, which means choosing 2 apples out of 5. Using the combination formula, we get: 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4 * 3!) / (2! * 3!) = (5 * 4) / (2 * 1) = 20 / 2 = 10.
So, there are 10 ways Sharon can choose 2 apples out of 5 apples.
Therefore, the probability of getting 2 apples is favorable outcomes / total outcomes = 10 / 8 = 5 / 4.
Hence, the probability that both fruits Sharon takes are apples is 5/4 in its simplest form.