a bag contains 12 black checkers and 12 red checkers. What is the probability of choosing two red checkers?
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Yours in incomplete.
You don't say how many checkers are chosen.
P(R1)=12/24 (first red)
P(R2)=11/23 (second red)
P(2*R)=(12/24)*(11/23)=11/46 (both red)
To find the probability of choosing two red checkers, we first need to calculate the total number of possible outcomes.
Step 1: Calculate the total number of checkers in the bag
The bag contains 12 black checkers and 12 red checkers, so the total number of checkers is 12 + 12 = 24.
Step 2: Calculate the number of ways to choose two red checkers
Since we only want to choose two red checkers, we need to calculate how many ways we can choose two items from the 12 red checkers. This can be done using the combination formula: C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items we want to choose.
Applying this formula, we get:
C(12, 2) = 12! / (2! * (12-2)!) = 12! / (2! * 10!) = (12 * 11) / (2 * 1) = 66.
Step 3: Calculate the number of ways to choose any two checkers from the bag
Since we want any two checkers, regardless of their color, we need to calculate how many ways we can choose two items from the 24 total checkers. This can also be calculated using the combination formula: C(n, r) = n! / (r! * (n-r)!).
Applying this formula, we get:
C(24, 2) = 24! / (2! * (24-2)!) = 24! / (2! * 22!) = (24 * 23) / (2 * 1) = 276.
Step 4: Calculate the probability of choosing two red checkers
The probability of an event is equal to the number of favorable outcomes divided by the number of possible outcomes.
In this case, the number of favorable outcomes is the number of ways to choose two red checkers, which is 66. The number of possible outcomes is the number of ways to choose any two checkers from the bag, which is 276.
So, the probability of choosing two red checkers is 66/276, which simplifies to 11/46.
Therefore, the probability of choosing two red checkers is 11/46.
To find the probability of choosing two red checkers from the bag, we need to find the ratio of the number of ways to choose two red checkers to the total number of possible outcomes.
Step 1: Determine the total number of checkers in the bag.
In this case, we have 12 black checkers and 12 red checkers, so the total number of checkers is 12 + 12 = 24.
Step 2: Determine the number of ways to choose two red checkers.
To choose two red checkers, we need to select 2 out of the 12 red checkers. This can be done using combinations, denoted as C(n, k), which is calculated as n! / (k! * (n-k)!), where n is the total number of items and k is the number of items we want to select. In this case, C(12, 2) = 12! / (2! * (12-2)!) = 66.
Step 3: Determine the total number of possible outcomes.
The total number of possible outcomes is the number of ways to choose any two checkers out of the 24 checkers in the bag. This can be calculated as C(24, 2) = 24! / (2! * (24-2)!) = 276.
Step 4: Calculate the probability.
The probability of choosing two red checkers is the ratio of the number of ways to choose two red checkers to the total number of possible outcomes. Therefore, the probability can be calculated as 66 / 276 = 11 / 46, which is approximately 0.2391 or 23.91%.
Therefore, the probability of choosing two red checkers from the bag is 11/46 or approximately 0.2391.