To solve this problem, we will follow these steps:
1. **Determine the total number of marbles**: According to the problem, there are 145 marbles in total.
2. **Count the non-blue marbles**: We are told there are 90 black marbles and 33 white marbles.
3. **Calculate the number of blue marbles**: Since we know the total number of marbles and the number of marbles of other colors, the number of blue marbles can be found by subtracting the number of black and white marbles from the total. This can be expressed as:
Number of blue marbles = Total marbles - Black marbles - White marbles
4. **Substitute the known values**: Plugging in the known values, we get:
Number of blue marbles = 145 (Total) - 90 (Black) - 33 (White)
Number of blue marbles = 145 - 90 - 33
Number of blue marbles = 55 - 33
Number of blue marbles = 22
So, there are 22 blue marbles in the bowl.
5. **Determine the probability**: The probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. For this problem, the favorable outcomes are pulling a blue marble, and the possible outcomes are pulling any marble.
Therefore, the probability of pulling a blue marble, P(Blue), is:
P(Blue) = Number of blue marbles / Total number of marbles
6. **Substitute the known values**: We can substitute the known values into the formula:
P(Blue) = 22 / 145
This is the probability of Jose pulling a blue marble from the bowl.
To have this in the simplest form, you can express the probability as a fraction, decimal or percentage:
As a fraction: 22/145 (This is already in its simplest form since 22 and 145 have no common factors other than 1).
As a decimal: To convert the fraction to a decimal, divide 22 by 145:
P(Blue) ≈ 0.1517 (rounded to four decimal places)
As a percentage: To convert the decimal to a percentage, multiply by 100:
P(Blue) ≈ 15.17% (rounded to two decimal places)
Therefore, the probability that Jose will pull a blue marble out of the bowl is 22/145, or about 15.17%.
