A box contains 3 red marbles, 4 white marbles, and 3 blue marbles. If a marble is drawn from the box at random, what is the probability that the marble is either red or blue?
Answer
Step 4: Because the events are mutually exclusive (drawing a red marble and drawing a blue marble cannot happen at the same time), we add the probabilities together to get the total probability. Therefore, the probability that the marble drawn is either red or blue is \(\frac{3}{10} + \frac{3}{10} = \frac{6}{10}\).
Step 1 ：Step 1: Identify the total number of outcomes. In this case, the total number of marbles is \(3 + 4 + 3 = 10\).
Step 2 ：Step 2: Identify the number of favorable outcomes for each of the two mutually exclusive events. The number of red marbles is 3 and the number of blue marbles is 3.
Step 3 ：Step 3: The probability of an event happening is the number of favorable outcomes divided by the total number of outcomes. So, the probability of drawing a red marble is \(\frac{3}{10}\) and the probability of drawing a blue marble is \(\frac{3}{10}\).
Step 4 ：Step 4: Because the events are mutually exclusive (drawing a red marble and drawing a blue marble cannot happen at the same time), we add the probabilities together to get the total probability. Therefore, the probability that the marble drawn is either red or blue is \(\frac{3}{10} + \frac{3}{10} = \frac{6}{10}\).
