Matt has a bag containing 12 green marbles and 8 blue marbles. Without looking, he pulls out one marbles and places it on the table. He then picks a second marbles from the bag. What is the probability he will have 2 blue marbles?
Probability= action×action
P= 8/20 × 7/19 (because one blue is gone)
P= 56/380
P= 14/95
To find the probability of picking two blue marbles, we need to consider the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. Matt needs to pick two blue marbles, so the number of favorable outcomes is the number of ways he can pick 2 blue marbles from the 8 blue marbles in the bag.
Number of favorable outcomes = Number of ways to choose 2 blue marbles from 8 blue marbles = C(8, 2)
C(n, r) represents the number of combinations of choosing r items from a set of n items, and it is calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
Applying this formula, we can calculate:
Number of favorable outcomes = C(8, 2) = 8! / (2!(8-2)!) = 8! / (2!6!) = (8 * 7) / (2 * 1) = 28
Now, let's determine the total number of possible outcomes. Matt has a total of 12 green marbles and 8 blue marbles in the bag, and he is picking 2 marbles.
Total number of possible outcomes = Number of ways to choose 2 marbles from 12 green marbles and 8 blue marbles = C(20, 2)
Number of favorable outcomes = 20! / (2!(20-2)!) = 20! / (2!18!) = (20 * 19) / (2 * 1) = 190
Finally, we can calculate the probability of picking two blue marbles by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 28 / 190 ≈ 0.147
Therefore, the probability that Matt will have 2 blue marbles is approximately 0.147, or 14.7%.
To find the probability of Matt getting 2 blue marbles, we need to determine how many possible outcomes there are and how many of those outcomes will result in 2 blue marbles.
First, let's find the total number of possible outcomes. Matt pulls out one marble and then another, so there are 20 marbles in total.
Next, let's find the number of outcomes where Matt gets 2 blue marbles. Since there are 8 blue marbles in the bag, the probability of getting a blue marble on the first draw is 8/20. After removing one blue marble, there are 7 blue marbles left out of 19 marbles. So, the probability of getting another blue marble on the second draw is 7/19.
To find the probability of both events happening, we multiply the probabilities together: (8/20) * (7/19) = 56/380.
Therefore, the probability of Matt getting 2 blue marbles is 56/380, which can be simplified to 7/47 or approximately 0.148.