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1 answer:
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Answer:
The probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.
Step-by-step explanation:
The complete question is:
Sophia made the following two-way table categorizing the US senators in 2015 by their political party and whether or not it was their first term in the senate.
Democratic Republican Independent Total
First Term 11 28 11 50
Returning 33 26 11 70
Total 44 54 22 120
Find the probability that the senator was in the Democratic party, given that the senator was returning to office.
Solution:
The conditional probability of an event <em>A</em> given that another event <em>X</em> has already occurred is given by:
The probability of an event <em>E</em> is given by the ratio of the number of favorable outcomes to the total number of outcomes.
Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:
Compute the probability of selecting an US senator who was returning to office as follows:
Compute the conditional probability, P (D | R) as follows:
Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.
Answer:
28 portraits
Step-by-step explanation:
Let's first figure out how many portraits Lamy can paint in 1 week, which is his <u>unit rate</u>. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.
In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is = 14 paintings per week.
Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a <u>directly proportional relationship</u>, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.
Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.
Hope this helps!