Simplify to create an equivalent expression. {2-4(5p+1)}2−4(5p+1)2, minus, 4, left parenthesis, 5, p, plus, 1, right parenthesis

Choose 1

(Choice A)
A
-20p-2−20p−2minus, 20, p, minus, 2

(Choice B)
B
-5p-4−5p−4minus, 5, p, minus, 4

(Choice C)
C
-20p+2−20p+2minus, 20, p, plus, 2

(Choice D)
D
-5p+4−5p+4

a) 0.4658 = 46.58% probability that the chosen ball is blue

b) 0.322 = 32.2% probability that it came from the first urn

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Conditional Probability

We use the conditional probability formula to solve this question. It 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.

a. What is the probability that the chosen ball is blue?

6/20 = 0.3 of 0.5(first urn)

12/19 = 0.6316 out of 0.5(second urn).

So

0.4658 = 46.58% probability that the chosen ball is blue.

b. If the chosen ball is blue, what is the probability that it came from the first urn?

Event A: Blue Ball

Event B: From first urn

From item a.,

Probability of blue ball from first urn:

0.3 of 0.5. So

Probability:

0.322 = 32.2% probability that it came from the first urn