High School

Welcome to the article The cup on my desk contains 3 red pens 4 blue pens 2 black pens 2 green pens and 1 orange pen If I randomly. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

The cup on my desk contains 3 red pens, 4 blue pens, 2 black pens, 2 green pens, and 1 orange pen. If I randomly select one pen to grade with, find the following probabilities:

a) P(green)

b) P(not red)

c) P(purple or orange)

Answer :

Sure! Let's go through the steps to find the required probabilities based on the contents of the cup:

1. Count the total number of pens:

In the cup, we have:
- 3 red pens
- 4 blue pens
- 2 black pens
- 2 green pens
- 1 orange pen

To find the total number of pens, we simply add up all of these:

[tex]\[
3 + 4 + 2 + 2 + 1 = 12 \text{ pens}
\][/tex]

2. Find each probability:

a) Probability of selecting a green pen, [tex]\( P(\text{green}) \)[/tex]:

There are 2 green pens in the cup. Therefore, the probability of selecting a green pen is calculated by dividing the number of green pens by the total number of pens:

[tex]\[
P(\text{green}) = \frac{2}{12} = \frac{1}{6} \approx 0.1667
\][/tex]

b) Probability of not selecting a red pen, [tex]\( P(\text{not red}) \)[/tex]:

First, we need to find the number of pens that are not red. Subtract the number of red pens from the total number of pens:

[tex]\[
12 - 3 = 9 \text{ pens not red}
\][/tex]

The probability is then:

[tex]\[
P(\text{not red}) = \frac{9}{12} = \frac{3}{4} = 0.75
\][/tex]

c) Probability of selecting a purple or orange pen, [tex]\( P(\text{purple or orange}) \)[/tex]:

In the cup, there are no purple pens and 1 orange pen. So, we only need to consider the orange pens:

[tex]\[
P(\text{purple or orange}) = \frac{0 + 1}{12} = \frac{1}{12} \approx 0.0833
\][/tex]

So, to summarize:
- The probability of selecting a green pen is approximately [tex]\( 0.1667 \)[/tex].
- The probability of not selecting a red pen is [tex]\( 0.75 \)[/tex].
- The probability of selecting a purple or orange pen is approximately [tex]\( 0.0833 \)[/tex].

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Rewritten by : Brahmana