4 kids have just received a large bag of candy pieces at a friend's birthday party each. The mean number of pieces of candy received in the bag per kid is 136. The numbers of pieces of candy for 3 of the kids are listed below. The number of pieces the fourth kid got is unknown. 164, 128, 132 Did the fourth kid receive more than, fewer than, or equal to 136 pieces? A More than 136 pieces B Fewer than 136 pieces Equal to 136 pieces
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Understanding Mean and Distribution of Values: An Educational Insight**
**Scenario:**
Four kids have just received a large bag of candy pieces at a friend's birthday party each. The mean number of pieces of candy received in the bag per kid is 136. The numbers of pieces of candy for 3 of the kids are listed below. The number of pieces the fourth kid got is unknown.
- 164, 128, 132
**Question:**
Did the fourth kid receive:
A) More than 136 pieces
B) Fewer than 136 pieces
C) Equal to 136 pieces
**Detailed Explanation:**
To find out whether the fourth kid received more, fewer, or equal to 136 pieces, we start by calculating the total number of pieces of candy, given that the mean per kid is 136.
1. **Calculating Total Pieces of Candy:**
The mean number of pieces is 136, and there are 4 kids.
\[
\text{Total pieces of candy} = \text{Mean} \times \text{Number of kids} = 136 \times 4 = 544 \text{ pieces}
\]
2. **Determining Pieces for the Fourth Kid:**
The numbers of pieces for 3 kids are: 164, 128, 132.
\[
\text{Sum of pieces for 3 kids} = 164 + 128 + 132 = 424 \text{ pieces}
\]
Given the total pieces of candy for all 4 kids, we can find out the pieces received by the fourth kid:
\[
\text{Number of pieces for the fourth kid} = \text{Total pieces} - \text{Sum of pieces for 3 kids} = 544 - 424 = 120 \text{ pieces}
\]
3. **Comparison with Mean:**
The fourth kid received 120 pieces of candy. Since 120 is less than the mean (136):
\[
\boxed{B) \text{Fewer than 136 pieces}}
\]
From the calculations, the answer to the question is that the fourth kid received fewer than 136 pieces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe608041-7614-44c8-9fb3-40788efd69dd%2F43fd4ef9-cbd3-450a-8ce2-0137be73d836%2Fmf9lz1b_processed.jpeg&w=3840&q=75)
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