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Sagot :
Using conditional probability, it is found that there is a 0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
- P(B|A) is the probability of event B happening, given that A happened.
- [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, the events are:
- Event A: President is left-handed.
- Event B: President is a democrat.
Researching the problem on the internet, it is found that:
- 40% of the presidents were left-handed, hence P(A) = 0.4.
- If a president is left-handed, there is a 13% chance that the president is a Democrat, hence P(B|A) = 0.13.
Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]0.13 = \frac{P(A \cap B)}{0.4}[/tex]
[tex]P(A \cap B) = 0.13(0.4)[/tex]
[tex]P(A \cap B) = 0.052[/tex]
0.052 = 5.2% probability that a randomly chosen U. S. President is left-handed and a democrat.
You can learn more about conditional probability at https://brainly.com/question/15536019
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