The probability of drawing a peppermint candy out of a jar of 25 candies is 1/5. How many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to 1/3?
(A) 5
(B) 10
(C) 15
(D) 30
If the probability of drawing is 1/5th out of 25 candies, then 25 x 1/5=5 peppermint candies in the jar. Let n be the number of candies to be added. Then:
1/3(25+n)=5+n
25/3+n/3=5+n
25+n=15+3n
10=2n
n=5
5 more peppermint candies need to be added.
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It's it A?
Hmm, let me calculate the probability of drawing a peppermint candy from the jar with the current amount. So, 1 out of 25 candies is peppermint, giving us a probability of 1/25.
Now, we want to increase the probability to 1/3. In order to do that, we need to add more peppermint candies to the jar. Let's say we add 'x' peppermint candies.
The new probability would be (1 + x) / (25 + x), and we want this to equal 1/3.
Solving the equation (1 + x) / (25 + x) = 1/3 for 'x', we get x = 10.
So, we need to add 10 more peppermint candies to the jar to increase the probability of drawing a peppermint candy to 1/3.
Therefore, the answer is (B) 10.
To solve this problem, we need to find out how many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to 1/3.
Let's assume that the number of peppermint candies initially in the jar is 'x'.
The probability of drawing a peppermint candy out of a jar of 25 candies is given as 1/5. This means that we have x peppermint candies out of a total of 25 candies, so we can write it as:
x/25 = 1/5
Now, we want to find the number of peppermint candies needed to increase the probability to 1/3. Let's call this number 'y'.
So after adding 'y' more peppermint candies, the new probability can be written as:
(x + y)/(25 + y) = 1/3
To solve this equation, we need to cross multiply:
3(x + y) = 25 + y
Expanding the equation:
3x + 3y = 25 + y
Simplifying by subtracting 'y' from both sides:
3x + 2y = 25
Now, let's substitute the initial probability equation into this equation:
3(1/5) + 2y = 25
Multiply through by 5 to get rid of the fraction:
3 + 10y = 125
Subtract 3 from both sides:
10y = 122
Divide by 10:
y = 12.2
Since we cannot have a fractional number of candies, we round 'y' up to the nearest whole number, which is 13.
Therefore, we should add 13 more peppermint candies to the jar in order to increase the probability of drawing a peppermint candy to 1/3.
The correct answer is (C) 15, as it is the closest available option to 13.
To solve this problem, we need to first calculate the current probability of drawing a peppermint candy, and then determine how many more peppermint candies need to be added to increase the probability to 1/3.
Step 1: Calculate the current probability of drawing a peppermint candy.
The current probability of drawing a peppermint candy is given as 1/5. This means that out of the 25 candies in the jar, 1 out of 5 is a peppermint candy. We can calculate the number of peppermint candies in the jar by multiplying the total number of candies by the probability.
Number of peppermint candies = Total number of candies * Probability
Number of peppermint candies = 25 * (1/5)
Number of peppermint candies = 5
So, currently, there are 5 peppermint candies in the jar.
Step 2: Determine how many more peppermint candies need to be added to increase the probability to 1/3.
Now, we need to find the number of candies required to increase the probability to 1/3. Let's assume we need to add x peppermint candies.
Revised probability of drawing a peppermint candy = (Number of peppermint candies + x) / (Total number of candies + x)
Revised probability of drawing a peppermint candy = 1/3
Now, let's solve for x:
(5 + x) / (25 + x) = 1/3
Cross-multiplying, we get:
3(5 + x) = 25 + x
15 + 3x = 25 + x
Simplifying the equation:
3x - x = 25 - 15
2x = 10
x = 5
So, you would need to add 5 more peppermint candies to the jar.
Therefore, the answer is (A) 5.