There are 4 blue marbles, 5 red marbles, 1 green marble, and 2 black marbles in a bag. Suppose you select one marble at random. Find each probability
there are lots of possible probabilities. For each color,
P(color) = #color/#total
so
P(red) = 5/(4+5+1+2) = 5/12
do the others similarly.
To find each probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.
1) Probability of selecting a blue marble:
Number of blue marbles = 4
Total number of marbles = 4 (blue) + 5 (red) + 1 (green) + 2 (black) = 12
Probability = 4/12 = 1/3
2) Probability of selecting a red marble:
Number of red marbles = 5
Total number of marbles = 12
Probability = 5/12
3) Probability of selecting a green marble:
Number of green marbles = 1
Total number of marbles = 12
Probability = 1/12
4) Probability of selecting a black marble:
Number of black marbles = 2
Total number of marbles = 12
Probability = 2/12 = 1/6
So, the probabilities are:
- Blue marble: 1/3
- Red marble: 5/12
- Green marble: 1/12
- Black marble: 1/6
To find each probability, we need to calculate the ratio of the favorable outcomes to the total number of outcomes.
1. Probability of selecting a blue marble:
The number of blue marbles is 4, and the total number of marbles is 4 + 5 + 1 + 2 = 12.
Therefore, the probability of selecting a blue marble is 4/12, which simplifies to 1/3.
2. Probability of selecting a red marble:
The number of red marbles is 5, so the probability of selecting a red marble is 5/12.
3. Probability of selecting a green marble:
There is only 1 green marble, so the probability of selecting a green marble is 1/12.
4. Probability of selecting a black marble:
There are 2 black marbles, so the probability of selecting a black marble is 2/12, which simplifies to 1/6.
Note: The sum of all probabilities should add up to 1, as 1 represents the total certainty of an event occurring.