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Probability and Tree Diagram
Probability is a measure of how likely something is to happen. This can expressed as a number, between 0 and 1, or as a percentage. Probability can calculated using a variety of methods, including counting, conditional probability, and Bayes’ theorem.
A tree diagram is a graphical tool used to calculate and visualize probabilities. It consists of a series of branches, each representing a possible outcome of a event. The branches are linked together, and the probabilities of each outcome are calculated. The tree diagram can used to calculate the probability of multiple events happening simultaneously, or the probability of one event occurring given the outcome of another event.
Where Tree Diagram Examples Used:
There many different places where tree diagrams can used. One common place is in mathematics, where tree diagrams used to represent the structure of a mathematical problem or equation. They can also used in biology to diagram the family tree of a particular species or to diagram the relationships between different species. In business, tree diagrams can used to map the hierarchy of a company or to diagram the supply chain for a product.
Tree Diagram in Probability
A tree diagram is a graphical representation of a probability distribution. It is a branching diagram that shows the possible outcomes of an event, and the probability of each outcome. The diagram starts with the event at the root, and then branches out to show the different outcomes. Each branch labelled with the probability of that outcome.
Calculating Overall Probability and Probability Tree Diagram
There is a 60% chance of rain tomorrow. This can calculated using the overall probability formula, which the probability of rain multiplied by the probability of not raining.
The probability of rain is 0.6 and the probability of not raining is 0.4, so the overall probability of it raining tomorrow 0.6 multiplied by 0.4, which equals 0.24.
A probability tree diagram can also used to calculate the overall probability. The first step is to draw a tree with one branch for rain and one branch for not raining. The next step is to calculate the probability of rain on the left side of the tree and the probability of not raining on the right side of the tree.
The probability of rain is 0.6 and the probability of not raining is 0.4, so the probability of rain on the left side of the tree is 0.6 and the probability of not raining on the right side of the tree is 0.4. The final step is to multiply the probabilities on the left and right sides of the tree to calculate the overall probability.
The probability of rain on the left side of the tree is 0.6 and the probability of not raining on the right side of the tree is 0.4, so the overall probability of it raining tomorrow 0.6 multiplied by 0.4, which equals 0.24.
Steps to Calculate Overall Probability
1. Add the probabilities of the individual events.
2. If the event is mutually exclusive, subtract the probability of the other event from 1.
3. If the events are not mutually exclusive, multiply the probabilities of the events.
