there are 20 apples and 15 oranges in a bin.if some apples are removed from the bin so that the probability of randomly drawing an apple becomes 2/5.how many apples must be removed from the bin
To find out how many apples must be removed from the bin, we can start by determining the probability of randomly drawing an apple before any apples are removed.
The total number of fruits in the bin is 20 apples + 15 oranges = 35 fruits.
The probability of randomly drawing an apple before any removals can be calculated as the ratio of the number of apples to the total number of fruits:
P(apple) = Number of apples / Total number of fruits
P(apple) = 20 / 35
We are given that the probability of randomly drawing an apple after the removal of some apples becomes 2/5. So, we can set up the equation:
P(apple after removals) = 2/5
We need to find the new number of apples after some are removed. Let's assume "x" represents the number of apples that are removed.
The new number of apples would be 20 - x (since x apples are being removed). The total number of fruits would then be (20 - x) + 15.
Using these values, we can calculate the new probability of randomly drawing an apple after removals:
P(apple after removals) = Number of apples after removals / Total number of fruits
P(apple after removals) = (20 - x) / [(20 - x) + 15]
Now, we can set up the equation using the given probability:
2/5 = (20 - x) / (35 - x)
To solve for x, we can cross-multiply:
2(35 - x) = 5(20 - x)
70 - 2x = 100 - 5x
Bringing the variable terms to one side:
5x - 2x = 100 - 70
3x = 30
Simplifying:
x = 30 / 3
x = 10
Therefore, 10 apples must be removed from the bin.
To solve this problem, we need to determine how many apples must be removed from the bin so that the probability of randomly drawing an apple becomes 2/5.
Step 1: Calculate the total number of fruits in the bin.
Given that there are 20 apples and 15 oranges, the total number of fruits in the bin is 20 + 15 = 35.
Step 2: Calculate the probability of randomly drawing an apple before any apples are removed.
The probability of randomly drawing an apple is the number of apples divided by the total number of fruits:
P(apple) = number of apples / total number of fruits = 20 / 35.
Step 3: Calculate the probability of randomly drawing an apple after removing some apples.
Let's assume x apples are removed. The new total number of fruits in the bin will be (20 - x) apples and 15 oranges. The probability of randomly drawing an apple is then:
P(apple) = (20 - x) / (35 - x).
Step 4: Set up an equation based on the given probability.
The problem states that the probability of randomly drawing an apple after removing some apples is 2/5. So we can set up the following equation:
(20 - x) / (35 - x) = 2/5.
Step 5: Solve the equation.
To solve the equation, we can cross multiply:
5(20 - x) = 2(35 - x).
Simplifying further:
100 - 5x = 70 - 2x.
Combine like terms:
-5x + 2x = 70 - 100.
-3x = -30.
Divide by -3:
x = 10.
Step 6: Interpret the result.
The solution x = 10 means that 10 apples must be removed from the bin in order for the probability of randomly drawing an apple to become 2/5.
Therefore, 10 apples must be removed from the bin.
2/5 = x/15
20 - x = ?