Part (a)
P(A) = 0.5
P(B) = 0.4
P(B/A) = 0.6
P(A and B) = P(A)*P(B/A)
P(A and B) = 0.5*0.6
P(A and B) = 0.3
<h3>Answer: 0.3</h3>
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Part (b)
We'll use the result from part (a)
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.5 + 0.4 - 0.3
P(A or B) = 0.6
<h3>Answer: 0.6</h3>
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Part (c)
A and B are not independent since P(B) does not equal P(B/A). The fact that event A happens changes the probability P(B). Recall that P(B/A) means "probability P(B) based on event A already happened". A and B are independent if P(B) = P(B/A).
Events A and B are not mutually exclusive since P(A or B) is not zero.
<h3>Answer: Neither</h3>
5. A. (4, -2)
6. C. (x, y) — (x, -y + 5)
Step-by-step explanation:
5. For the formula y = x, the x and y coordinates get swapped.
M = (-2, 4) — M’ = (4, -2)
6. If the coordinates get reflected across the x-axis, the y coordinates become negative.
(x, y) — (x, -y)
Now that the coordinates are reflected, you go 5 units up (+ 5) to get to the reflection of the coordinates if it was 5 units down before it reflected across the x-axis (- 5).
Ex. 1, 6 gets reflected across the x-axis and moved 5 units up. It’s reflection would be equivalent to (1, -1) because it moved 5 units down (1, 1) then reflected across the x-axis (1, -1).
(x, y - 5) reflected across the x-axis is equivalent to (x, -y + 5)
At least 4
10% of 12 is 1.2
So 30% is 3.6
And 1% 0.12
So 2% is 0.24
Plus 3.6 onto 0.24 and you get 3.84
The answer is: " 40 books " .
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Explanation:
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Let "x" equal the number of books that Jill started with. Solve for "x" :
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x – (1/2)x + 16 = 36 ;
1x – (1/2)) = (1/2)x ;
(1/2)x + 16 = 36 ;
Subtract "16" from EACH SIDE of the equation:
(1/2)x + 16 – 16 = 36 – 16 ;
(1/2)x = 20 ;
Multiply each side of the equation by "2" ;
2*(1/2)x = 20 * 2 ;
to get: x = 40 .
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The answer is: " 40 books " .
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