The probability of rolling an even number of a die and drawing a red marble from a bag containing 3 red marble and 5 green marbles must be expressed as a reduced fraction of the form a/b
what is the value of a and b?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events, not dividing.
Fraction = desired event/total possibilities
die = 3/6
Marble = 3/8
To find the probability of rolling an even number on a die and drawing a red marble, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of favorable outcomes:
- Rolling an even number on a die: Out of the six possible outcomes (numbers 1-6), three of them are even (2, 4, and 6).
- Drawing a red marble: The bag contains a total of 3 red marbles.
Since these two events are independent, we can multiply the probabilities of each event to get the total number of favorable outcomes:
Favorable outcomes = (3/6) * (3/8)
Next, let's determine the total number of possible outcomes:
- Rolling any number on a die: Out of the six possible outcomes (numbers 1-6), each has an equal chance of occurring.
- Drawing any marble from the bag: The bag contains a total of 3 red marbles and 5 green marbles.
Again, since these two events are independent, we can multiply the probabilities of each event to get the total number of possible outcomes:
Possible outcomes = (6/6) * (8/8)
To express the probability as a reduced fraction, we simplify the fraction by canceling out any common factors between the numerator and denominator.
Simplifying the fraction (3/6) * (3/8):
- The numerator (3) has a common factor of 3 with the denominator (6), so we can simplify it to 1.
- The numerator (3) and denominator (8) do not share any common factors.
So the probability can be expressed as the reduced fraction 1/8.
Therefore, the value of a is 1 and the value of b is 8.