Probability of Pulling a Purple and Then a Pink Hair Bow

Oct 13, 2025 by talynt.org 96 views

Probability of Pulling a Purple and Then a Pink Hair Bow

In this article, we will explore the concept of probability and how it applies to a real-life scenario. Lily is trying to find a pink hair bow in her drawer, but she has a total of 27 bows in different colors. We will calculate the probability that she pulls out a purple bow, puts it back, and then pulls out a pink bow.

Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this case, we want to find the probability that Lily pulls out a purple bow, puts it back, and then pulls out a pink bow.

To calculate the probability, we need to consider two events: pulling out a purple bow and pulling out a pink bow. We will use the formula for conditional probability, which is:

P(A and B) = P(A) × P(B|A)

where P(A) is the probability of event A occurring, and P(B|A) is the probability of event B occurring given that event A has occurred.

Step 1: Calculate the Probability of Pulling Out a Purple Bow

First, we need to calculate the probability of pulling out a purple bow. There are 3 purple bows out of a total of 27 bows. So, the probability of pulling out a purple bow is:

P(purple) = Number of purple bows / Total number of bows = 3 / 27 = 1/9

Step 2: Calculate the Probability of Pulling Out a Pink Bow Given That a Purple Bow Has Been Pulled Out

Next, we need to calculate the probability of pulling out a pink bow given that a purple bow has been pulled out. Since the purple bow has been put back, the total number of bows remains the same, which is 27. However, the number of pink bows remains the same, which is 15. So, the probability of pulling out a pink bow given that a purple bow has been pulled out is:

P(pink|purple) = Number of pink bows / Total number of bows = 15 / 27 = 5/9

Step 3: Calculate the Probability of Pulling Out a Purple Bow and Then a Pink Bow

Now, we can calculate the probability of pulling out a purple bow and then a pink bow using the formula for conditional probability:

P(purple and pink) = P(purple) × P(pink|purple) = 1/9 × 5/9 = 5/81

In conclusion, the probability that Lily pulls out a purple bow, puts it back, and then pulls out a pink bow is 5/81. This means that there is a 5% chance that she will pull out a purple bow and then a pink bow.

The concept of probability is used in many real-world applications, such as:

Insurance: Insurance companies use probability to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
Finance: Financial institutions use probability to calculate the likelihood of a stock or a bond performing well or poorly.
Medicine: Medical professionals use probability to calculate the likelihood of a patient recovering from a disease or experiencing a side effect from a medication.

In our previous article, we explored the concept of probability and how it applies to a real-life scenario. We calculated the probability that Lily pulls out a purple bow, puts it back, and then pulls out a pink bow. In this article, we will answer some frequently asked questions related to probability and the scenario we discussed earlier.

Q: What is the probability of pulling out a purple bow and then a pink bow?

A: The probability of pulling out a purple bow and then a pink bow is 5/81, which is approximately 0.06 or 6%.

Q: What is the probability of pulling out a pink bow given that a purple bow has been pulled out?

A: The probability of pulling out a pink bow given that a purple bow has been pulled out is 5/9, which is approximately 0.56 or 56%.

Q: What is the probability of pulling out a purple bow given that a pink bow has been pulled out?

A: The probability of pulling out a purple bow given that a pink bow has been pulled out is 3/27, which is approximately 0.11 or 11%.

Q: What is the total number of bows in the drawer?

A: The total number of bows in the drawer is 27.

Q: How many purple bows are there in the drawer?

A: There are 3 purple bows in the drawer.

Q: How many pink bows are there in the drawer?

A: There are 15 pink bows in the drawer.

Q: What is the probability of pulling out a red bow?

A: The probability of pulling out a red bow is 9/27, which is approximately 0.33 or 33%.

Q: What is the probability of pulling out a purple bow and then a red bow?

A: The probability of pulling out a purple bow and then a red bow is (1/9) × (9/27), which is approximately 0.037 or 3.7%.

Q: What is the probability of pulling out a pink bow and then a red bow?

A: The probability of pulling out a pink bow and then a red bow is (15/27) × (9/27), which is approximately 0.44 or 44%.

In conclusion, we have answered some frequently asked questions related to probability and the scenario we discussed earlier. We hope that this article has provided you with a better understanding of probability and how it applies to real-life scenarios.

The concept of probability is used in many real-world applications, such as:

Insurance: Insurance companies use probability to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
Finance: Financial institutions use probability to calculate the likelihood of a stock or a bond performing well or poorly.
Medicine: Medical professionals use probability to calculate the likelihood of a patient recovering from a disease or experiencing a side effect from a medication.

In this article, we have explored the concept of probability and how it applies to a real-life scenario. We have answered some frequently asked questions related to probability and the scenario we discussed earlier. We hope that this article has provided you with a better understanding of probability and how it applies to real-life scenarios.