A jar contains 6 red, 7 white, and 7 blue marbles. If a marble chosen at random. Find the following probabilities?
A)P(red)
B)P(white)
C)P(red or blue)
D)P(red and white)
For A and B, just divide the number of your color by the total. For example,
P(blue) = 7/20
D is a trick question.
A) To find the probability of selecting a red marble, we need to divide the number of red marbles by the total number of marbles in the jar.
There are 6 red marbles out of a total of 6 + 7 + 7 = 20 marbles.
P(red) = 6/20 = 3/10
B) Similarly, to find the probability of selecting a white marble:
There are 7 white marbles out of a total of 20 marbles.
P(white) = 7/20
C) To find the probability of selecting either a red or a blue marble, we need to add the probabilities of selecting a red marble and a blue marble.
P(red or blue) = P(red) + P(blue)
Since we already calculated P(red) as 3/10, we need to find P(blue).
There are 7 blue marbles out of a total of 20 marbles.
P(blue) = 7/20
P(red or blue) = P(red) + P(blue) = 3/10 + 7/20 = (6/20) + (7/20) = 13/20
D) To find the probability of selecting both a red and a white marble, we need to multiply the probabilities of selecting a red marble and a white marble.
P(red and white) = P(red) × P(white)
P(red) = 3/10 (already calculated)
There are 7 white marbles out of a total of 20 marbles.
P(white) = 7/20
P(red and white) = (3/10) × (7/20) = 21/200
To find the probabilities, we need to understand a few basic concepts:
1. Total Number of Marbles: The jar contains a total of 6 red + 7 white + 7 blue = 20 marbles.
2. P(Event): The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Now, let's find the probabilities:
A) P(red):
The number of favorable outcomes (red marbles) is 6, and the total number of possible outcomes (total number of marbles) is 20.
P(red) = 6/20 = 0.3
B) P(white):
Similar to part A, the number of favorable outcomes (white marbles) is 7, and the total number of possible outcomes (total number of marbles) is 20.
P(white) = 7/20 = 0.35
C) P(red or blue):
To find the probability of picking a red or blue marble, we sum the number of red (6) and blue (7) marbles:
Number of favorable outcomes = 6 (red) + 7 (blue) = 13
P(red or blue) = 13/20 = 0.65
D) P(red and white):
Since there are no marbles that are both red and white, the probability of picking a marble that is both red and white is 0.
P(red and white) = 0
I hope this helps! Let me know if you have any further questions.