#1: A couple plans on having 3 children, how do I create a tree diagram with 8 possible outcomes?
#2: (What is the theoretical probability of having a girl, and what is the theoretical probability of having a boy?)
#3: How do you do theoretical probability?
The sex ratio at birth worldwide is commonly thought to be 107 boys to 100 girls, although this value is subject to debate in the scientific community. The sex ratio for the entire world population is 101 males to 100 females.
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#1: To create a tree diagram with 8 possible outcomes for a couple planning to have 3 children, you can follow these steps:
1. Start by drawing a horizontal line. This will represent the first child.
2. From the first child, draw three branches extending outwards. Label each branch with one of the possible outcomes: "Boy" or "Girl".
3. For each branch representing a "Boy" or a "Girl," draw three more branches extending outwards from it. Label each branch with one of the possible outcomes: "Boy" or "Girl".
4. Repeat this step for all the branches representing the previous child. In the end, you will have a total of 8 branches representing all the possible outcomes for the three children.
The resulting tree diagram should look like this:
First child
/ \
Boy Girl
/ \ / \
Boy Girl Boy Girl
| | | |
Boy Girl Boy Girl
#2: The theoretical probability of having a girl is 1/2, while the theoretical probability of having a boy is also 1/2. This means that for each child, there is an equal chance of having either a boy or a girl.
In probability, theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, since having a girl and having a boy are equally likely outcomes, the probability of each is 1/2.
#3: Theoretical probability is a way to determine the likelihood of an event occurring based on logical reasoning or assumptions, without actually conducting any experiments or observations. It is calculated by dividing the number of favorable outcomes (outcomes that meet the desired criteria) by the total number of possible outcomes.
To calculate the theoretical probability of an event, follow these steps:
1. Determine the number of favorable outcomes - these are the outcomes that meet the desired criteria.
2. Determine the total number of possible outcomes - these are all the possible outcomes, including the favorable ones.
3. Divide the number of favorable outcomes by the total number of possible outcomes.
4. Simplify the fraction if necessary.
The result will be the theoretical probability of the event occurring, usually expressed as a fraction or a decimal.