Question

What is the probability that a randomly chosen u. S. President is left-handed and a democrat?.

Answer 1

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:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ 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:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.13 = \frac{P(A \cap B)}{0.4}$

$P(A \cap B) = 0.13(0.4)$

$P(A \cap B) = 0.052$

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 brainly.com/question/15536019