The proportion of red marbels in a large jar of red and black marbels is 0.4 and the percentage of damaged red and black marbels is 0.7.

What is the probability of selecting randomly a black and damaged marbel?

If you randomly select three marbels, what is the probability of selecting a red OR a black marbel?

If you select five at random what is the probability of selecting at least one of each color?

To find the probability of selecting a black and damaged marble, we need to multiply the proportion of black marbles by the percentage of damaged marbles, assuming the two events are independent.

Step 1: Calculate the probability of selecting a black marble.
The proportion of black marbles is given as 1 - 0.4 = 0.6

Step 2: Calculate the probability of selecting a damaged marble.
The percentage of damaged marbles is given as 0.7

Step 3: Multiply the probabilities calculated in steps 1 and 2 to get the probability of selecting a black and damaged marble.
Probability = 0.6 * 0.7 = 0.42 or 42%

To calculate the probability of selecting a red OR a black marble when randomly selecting three marbles, we need to calculate the probability of selecting a red marble, the probability of selecting a black marble, and then add those probabilities together.

Step 1: Calculate the probability of selecting a red marble.
The proportion of red marbles is given as 0.4

Step 2: Calculate the probability of selecting a black marble.
The proportion of black marbles is given as 0.6

Step 3: Add the probabilities calculated in steps 1 and 2 to get the probability of selecting a red OR a black marble.
Probability = 0.4 + 0.6 = 1 or 100%

To calculate the probability of selecting at least one of each color when randomly selecting five marbles, we can calculate the complement of the probability of selecting none of each color.

Step 1: Calculate the probability of selecting no red marbles.
The probability of selecting no red marbles is given by (1 - 0.4)^5 = 0.6^5 = 0.07776 or 7.776%

Step 2: Calculate the probability of selecting no black marbles.
The probability of selecting no black marbles is given by (1 - 0.6)^5 = 0.4^5 = 0.01024 or 1.024%

Step 3: Calculate the complement of selecting none of each color.
The complement is given by 1 - (probability of selecting no red marbles) * (probability of selecting no black marbles).
Probability = 1 - (0.07776 * 0.01024) = 1 - 0.0007969 = 0.9992031 or 99.92%