Solved on Nov 13, 2023

Probability of randomly selecting a red marble from a bag with 8 marbles (4 red, 3 yellow, 1 blue).
Solution: P(red)=48=12P(\text{red}) = \frac{4}{8} = \frac{1}{2}

STEP 1

Assumptions1. The bag contains8 marbles in total. . There are4 red marbles,3 yellow marbles, and1 blue marble.
3. A marble is chosen at random, meaning each marble has an equal chance of being chosen.

STEP 2

The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the favorable outcome is choosing a red marble, and the total outcomes are the total number of marbles.
Probability=NumberoffavorableoutcomesTotalnumberofoutcomesProbability = \frac{Number\, of\, favorable\, outcomes}{Total\, number\, of\, outcomes}

STEP 3

Now, plug in the given values for the number of favorable outcomes (number of red marbles) and the total number of outcomes (total number of marbles) to calculate the probability.
Probability=NumberofredmarblesTotalnumberofmarblesProbability = \frac{Number\, of\, red\, marbles}{Total\, number\, of\, marbles}

STEP 4

Substitute the values into the equation.
Probability=48Probability = \frac{4}{8}

STEP 5

implify the fraction to its simplest form.
Probability=12Probability = \frac{1}{2}The probability that the marble chosen at random is red is1/2.

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