Solve the given problem that involves probability

In summary, the tree diagram breaks down the events and outcomes in a problem to help calculate the probabilities. In the given problem, we can use the tree diagram to find the probability of event B given that event A has not occurred, and then use that to solve for the probability of event B and event A occurring together. This results in a probability of 7/12 for event A given that event B has occurred.
  • #1
chwala
Gold Member
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Homework Statement
See attached
Relevant Equations
Probability
1677755033297.png


I would like to know how one can use the tree diagram...hence my post... otherwise, i was able to solve problem as follows,

a. ##P(A∩B)= \dfrac{3}{4} ×\dfrac{1}{5}=\dfrac{3}{20}##

b. ## P(B/A')=\dfrac{P(B)-\dfrac{3}{20}}{P(A')}##

##\dfrac{3}{7}=\dfrac{P(B)-\dfrac{3}{20}}{\dfrac{1}{4}}##

...

##P(B)=\dfrac{9}{35}##

c. ## P(A/B)=\dfrac{3}{20} ×\dfrac{35}{9}=\dfrac{7}{12}##
 

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  • #2
chwala said:
Homework Statement:: See attached
Relevant Equations:: Probability

View attachment 323090

I would like to know how one can use the tree diagram...hence my post... otherwise, i was able to solve problem as follows,

a. ##P(A∩B)= \dfrac{3}{4} ×\dfrac{1}{5}=\dfrac{3}{20}##

b. ## P(B/A')=\dfrac{P(B)-\dfrac{3}{20}}{P(A')}##

##\dfrac{3}{7}=\dfrac{P(B)-\dfrac{3}{20}}{\dfrac{1}{4}}##

...

##P(B)=\dfrac{9}{35}##

c. ## P(A/B)=\dfrac{3}{20} ×\dfrac{35}{9}=\dfrac{7}{12}##
See Conditional Probability Tree at https://www.cuemath.com/data/probability-tree-diagram/
 

1. What is probability and how is it used in problem solving?

Probability is the measure of the likelihood of an event occurring. It is used in problem solving to determine the chances of a certain outcome happening and to make informed decisions based on those chances.

2. How do you calculate probability?

To calculate probability, you divide the number of favorable outcomes by the total number of possible outcomes. This will give you a decimal or fraction that represents the likelihood of the event occurring.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual trials or experiments and may differ from the theoretical probability due to chance or other factors.

4. How can you use probability to solve real-life problems?

Probability can be used to make predictions and decisions in real-life situations, such as weather forecasting, risk assessment, and game strategies. It can also help in understanding and interpreting data in fields like economics, medicine, and social sciences.

5. What are some common misconceptions about probability?

One common misconception is that past events can affect the outcome of future events. In reality, each event is independent and the probability remains the same. Another misconception is that the higher the number of trials, the closer the experimental probability will be to the theoretical probability. This is not always the case and can vary depending on the situation.

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