Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one pen at random from his backpack, what is the probability that the pen is either red or black?
(A) \(\frac{2}{3}\)
(B) \(\frac{3}{5}\)
(C) \(\frac{2}{5}\)
(D) \(\frac{1}{3}\)
Answer (2)
Calculate the total number of pens: 5 + 6 + 4 = 15 .
Calculate the number of red or black pens: 6 + 4 = 10 .
Calculate the probability of picking a red or black pen: 15 10 .
Simplify the fraction to find the final probability: 3 2 .
Explanation
Find the total number of pens Let's first find the total number of pens in Marty's backpack. He has 5 blue pens, 6 black pens, and 4 red pens. So, the total number of pens is:
Calculate the total 5 + 6 + 4 = 15
Find the number of red or black pens Next, we want to find the number of pens that are either red or black. He has 6 black pens and 4 red pens. So, the number of red or black pens is:
Calculate the number of red or black pens 6 + 4 = 10
Calculate the probability Now, we can find the probability that the pen Marty pulls out is either red or black. The probability is the number of red or black pens divided by the total number of pens:
Simplify the fraction 15 10 = 3 2
State the final answer So, the probability that the pen Marty pulls out is either red or black is 3 2 .
Examples
Imagine you have a bag of marbles with different colors, and you want to know the chance of picking a marble of a specific color. This is similar to calculating probabilities in games, surveys, or any situation where you want to predict the likelihood of an event happening. For example, if you're designing a game with colored tokens, you can use probability to balance the game and make sure certain outcomes are more or less likely.
The probability that the pen Marty pulls out is either red or black is 3 2 . This is calculated by determining the total number of pens and the number of red or black pens. Therefore, the correct answer is option (A) 3 2 .
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