Mathematics, 20.07.2019 14:30 ava789

The probability that a student correctly answers on the first try (the event a. is p(a) = 0.2. if the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event b). the probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.5. find the probability that the student answers the question on the first or second try. a.0.90 b.0.40 c.0.10 d.0.70 e.0.60

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Answer from: tednequamoore4307

The probability that the student answers the question on the first or second try is 0.60.

Given

P(A) = 0.2

$\rm P(B|A^c)=0.5$ .

What is conditional probability?

The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.

When two events are mutually exclusive.

Then,

$\rm P(A\cap B)=0$

The first probability is;

$\rm P(A^C)=1-0.2=0.8$

Therefore,

The probability that the student answers the question on the first or second try is;

$\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60$

Hence, the probability that the student answers the question on the first or second try is 0.60.

To know more about Conditional probability click the link given below.

link

Answer from: drandbone92

Note that the two events are mutually exclusive. If the question is answered correctly on the first try, there's no need to give it another attempt. So $\mathbb P(A\cap B)=0$ .

We're given that P(A)=0.2

and $P(B\mid A^C)=0.5$ . From the first probability, we know that P(A^C)=1-0.2=0.8

. By definition of conditional probability,

$\mathbb P(B\mid A^C)=\dfrac{\mathbb P(B\cap A^C)}{\mathbb P(A^C)}$
$\implies\mathbb P(B\cap A^C)=0.5\cdot0.8=0.4$

We're interested in the probability of either

occurring, i.e. $\mathbb P(A\cup B)$ . Apply the inclusion-exclusion principle, which says

$\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)$

We know the probability of intersection is 0, and we know $\mathbb P(A)$ . Meanwhile, by the law of total probability, we have

$\mathbb P(B)=\mathbb P(B\cap A)+\mathbb P(B\cap A^C)=\mathbb P(B\cap A^C)$

so we end up with

$\mathbb P(A\cup B)=0.2+0.4=0.6$

Answer from: Quest

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b): y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4 perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

Which equation represents a line perpendicular to the line shown on the graph?

Answer from: Quest

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right

Which graph represents the solution set of the inequality x+2> 6

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