Janet has a jar with 8 gold marbles 12 silver marbles and 4 bronze marbles is she chooses two marbles without replacement, what is the probability that she chooses two silver marbles.
I think the answer is 11/46 but not sure how to work the prboem
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
12/24 * (12-1)/(24-1) = ?
To calculate the probability, we need to find the total number of possible outcomes and the number of favorable outcomes.
Step 1: Find the total number of marbles in the jar.
Total number of marbles = 8 (gold) + 12 (silver) + 4 (bronze) = 24
Step 2: Find the number of favorable outcomes (choosing two silver marbles).
We need to choose 2 silver marbles from a total of 12.
So, using the combination formula, the number of favorable outcomes (C) is given by:
C(12, 2) = 12! / (2! * (12-2)!) = 66
Step 3: Find the total number of possible outcomes (choosing any 2 marbles).
We need to choose 2 marbles from a total of 24.
Again, using the combination formula, the total number of possible outcomes (T) is given by:
T(24, 2) = 24! / (2! * (24-2)!) = 276
Step 4: Calculate the probability by dividing the number of favorable outcomes by the number of total outcomes.
Probability = C / T = 66 / 276 = 11/46
So, you were correct! The probability that Janet chooses two silver marbles is indeed 11/46.
To find the probability of Janet choosing two silver marbles, we first need to calculate the total number of possible outcomes (sample space) and the number of favorable outcomes (choosing two silver marbles).
The total number of marbles in the jar is 8 (gold) + 12 (silver) + 4 (bronze) = 24 marbles.
To calculate the probability of choosing two silver marbles from the jar without replacement, we can use the following formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes or sample space)
The first silver marble can be chosen from a pool of 12 silver marbles, and the second silver marble can be chosen from 11 remaining silver marbles. Since the marbles are drawn without replacement, the number of favorable outcomes is the number of ways to choose two silver marbles from the 12 available, which is the combination function.
The number of ways to choose two silver marbles from 12 is:
12C2 = (12!)/(2!(12-2)!) = (12!)/(2!10!) = (12 × 11)/(2 × 1) = 66
The total number of possible outcomes or sample space is the total number of ways to choose any two marbles from 24:
24C2 = (24!)/(2!(24-2)!) = (24!)/(2!22!) = (24 × 23)/(2 × 1) = 276
Now we can calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes or sample space)
Probability = 66 / 276
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 6), we get:
Probability = 11 / 46
So, the probability that Janet chooses two silver marbles from the jar without replacement is 11/46.