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Find the probability that the senator was in the Democratic party, given that the senator was returning to office.

shutvik [7]

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 A given that another event X has already occurred is given by:

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

The probability of an event E is given by the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:

$P(D\cap R)=\frac{33}{120}=0.275$

Compute the probability of selecting an US senator who was returning to office as follows:

$P(R)=\frac{70}{120}=0.5833$

Compute the conditional probability, P (D | R) as follows:

$P(D|R)=\frac{P(D\cap R)}{P(R)}$

$=\frac{0.275}{0.5833}\\\\=0.4714555\\\\\approx 0.4715$

Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

4 0

3 years ago

Read 2 more answers

Kelly solved an equation: H/ 4 - 11 = 13 using two inverse operations of adding 11 to both sides of the equations, and then divi

MariettaO [177]

Answer:

She should have multiplied by 4, not divided

Step-by-step explanation:

Given

$\frac{H}{4}$ - 11 = 13 ( add 11 to both sides ) ← correct

$\frac{H}{4}$ = 24 ( multiply both sides by 4 to clear the fraction )

H = 4 × 24 = 96

H is divided by 4, thus the inverse operation is to multiply

6 0

2 years ago

Which number of solutions is not possible for a system of two linear equations?

diamong [38]

Systems of linear equations can only have 0, 1, or an infinite number of solutions. These two lines cannot intersect twice. The correct answer is that the system has one solution.

7 0

3 years ago

Factor the following Polynomials 2x2 + 5x + 2

Leokris [45]

Answer:

Step-by-step explanation:

Find the multiples of 2x^2 and 2

for 2x^ you get 2,1 but they need to have x to get x^2 so; (2x and x)=2x^2

for 2 you get 2,1 (2x1)=2

Because your equation has a 5x and no negatives you know that your factors need to be positive.

(2x+1)(x+2)

when you multiply these you get

2x^2+4x+x+2 (remember 2x multiplies with everything inside (x+2) = 2x^2+4) and so on for the x (x+2) =x+2 )

Then you combine like terms 4x+x=5x

and those are the only like terms available and you get

2x^2+5x+2

Hope it helped

3 0

2 years ago

ANSWER QUICKLY 14 PTS FOR WHOEVER ANSWERS!

miv72 [106K]

Answer:

PAST

Step-by-step explanation:

the words "taught" and "yesterday" are in the past tense.

5 0

3 years ago

Read 2 more answers