If there are 2 yellow, 3 purple, 1 pink, 2 orange, and 2 black marbles in a bag, find the
probability of randomly selecting a pink and a black marble.
To find the probability of randomly selecting a pink and a black marble from the given set of marbles, we need to find the ratio of the number of favorable outcomes to the total number of possible outcomes.
Step 1: Determine the total number of marbles.
Count the number of marbles in the bag: 2 yellow + 3 purple + 1 pink + 2 orange + 2 black = 10 marbles
Step 2: Determine the number of favorable outcomes.
We want to select one pink marble and one black marble. There is only one pink marble and two black marbles in the bag. So, we have 1 pink marble * 2 black marble = 2 favorable outcomes.
Step 3: Determine the total number of possible outcomes.
The total number of marbles in the bag is 10, so there are 10 possible outcomes.
Step 4: Calculate the probability.
The probability is the ratio of favorable outcomes to the total number of possible outcomes.
Probability = favorable outcomes / total outcomes
In this case, the probability of randomly selecting a pink and a black marble is:
Probability = 2 favorable outcomes / 10 total outcomes
Probability = 1/5 or 0.2
Therefore, the probability of randomly selecting a pink and a black marble is 0.2 or 1/5.
To find the probability of randomly selecting a pink and a black marble, we need to know the total number of marbles in the bag and the number of pink and black marbles.
Given:
- 2 yellow marbles
- 3 purple marbles
- 1 pink marble
- 2 orange marbles
- 2 black marbles
To find the probability, we'll need the total number of marbles and the number of pink and black marbles.
Total number of marbles = 2 yellow + 3 purple + 1 pink + 2 orange + 2 black = 10 marbles
Number of pink marbles = 1
Number of black marbles = 2
To calculate the probability, we divide the number of desired outcomes (pink and black marbles) by the total number of possible outcomes (all marbles).
Therefore, probability = (Number of pink marbles / Total number of marbles) * (Number of black marbles / (Total number of marbles - 1))
Probability = (1/10) * (2/9)
Probability = 1/45
So, the probability of randomly selecting a pink and a black marble is 1/45.
total marbles: 2+3+1+2+2 = 10
P(pink,black) = 1/10 * 2/9
P(black,pink) = 2/9 * 1/10
now add 'em up, since these are mutually exclusive events.