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3 years ago

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A group of research proposals was evaluated by a panel of experts to decide whether or not they were worthy of funding. When the

se same proposals were submitted to a second independent panel of experts, the decision to fund was reversed in 40% of the cases. If the probability that a proposal is judged worthy of funding by the first panel is 0.3, what are the probabilities of these events

1 answer:

alukav5142 [94]3 years ago

3 0

Answer:

Let A represent the event that the first group approves the proposal.

Let B represent the event that the second group approves the proposal.

We know the following:

P(A) = 0.3

P(B given A) = 1 - 0.3 = 0.7

P(not B given not A) = 1 - 0.3 = 0.7 .

A) P(approved by both groups)

= P(A and B)

= P(A)P(B given A)

= 0.3(0.7)

= 0.21 .

B) P(disapproved by both groups)

= P(not A and not B)

= P(not A)P(not B given not A)

= (1 - 0.3)(0.7)

= 0.49 .

C) This problem might be ambiguous...do you mean exactly one group or at least one group? So, I will use both interpretations.

P(approved by at least one group)

= 1 - P(disapproved by both groups)

= 1 - 0.49

= 0.51 .

P(approved by exactly one group)

= P(second group reverses the first group's decision)

= 0.4 .

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When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.

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Two events A and B are said to be independent iff we have:

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Comparing it with chain rule will give

P(A|B) = P(A)

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The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

The options given are as follows:

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Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

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The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

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From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

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Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.

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