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.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula is:

In which
- P(B|A) is the probability of event B happening, given that A happened.
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:




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
The least weight of a bag in the top 5 percent of the distribution is; 246
From the complete question below, we are given;
Population mean; μ = 240
Population standard deviation; σ = 3
Z-score formula is;
z = (x' - μ)/σ
- Now, we want to find the least weight in the top 5 of the distribution and as such we will use;
1 - 0.05/2 = 0.025 as significance level
Z-score at significance level of 0.025 is 1.96
Thus;
1.96 = (x' - 240)/3
3 × 1.96 = x' - 240
x' = 240 + 5.88
x' = 245.88
Approximating to a whole number gives;
x' = 246
Complete question is;
A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?
Read more about z-score at; brainly.com/question/25638875
The answer to this question is 22.