2/3 of a page in 5/12 of a minute
Multiply both fractions by 3/2


So,
Ethan can read 1 page in 5/8 of a minute.
Any number from -10 to -∞ would be correct. One example is -79.
Answers:
- (a) Independent
- (b) Dependent
- (c) Dependent
- (d) Independent
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Explanation:
If events A and B are independent, then the two following equations must both be true
- P(A | B) = P(A)
- P(B | A) = P(B)
This is because the conditional probability P(A|B) means "P(A) when B has happened". If B were to happen, then P(A) must be the same as before. In other words, event B does not affect A, and vice versa.
For part (a), we have P(B) = 1/4 and P(B|A) = 1/4 showing that P(B|A) = P(B) is true, and therefore we can say the events are independent. We don't need the info that P(A) = 1/8.
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Unlike part (a), part (b) has the answer "dependent" because P(A) = 1/8 and P(A | B) = 1/3 differ in value. Event A starts off at probability 1/8, but then event B occurring means P(A) gets increased to 1/3. The prior knowledge about B changes the chances of A. The P(B) = 1/5 is unneeded.
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If A and B were independent, then,
P(A and B) = P(A)*P(B)
However,
P(A)*P(B) = (1/4)*(1/5) = 1/20
which is not the same as P(A and B) = 1/6. Therefore the two events are dependent.
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Refer back to part (a)
P(A) = 1/4 and P(A|B) = 1/4 are identical in value, so P(A|B) = P(A) which leads to the events being independent. Whether we know event B happened or not, it does not affect the outcome of event A. P(B) = 1/9 is unneeded.
You need to use the grids to draw rectangles which meet the requirements to help you put the answers in on the right.
1) Short side of 7 and long side of 9.
2) Short side of 9 and long side of 10.
3) Short side of 3 and long side of 8.
4) Short side of 4 and long side of 9.
5) Short side of 3 and long side of 5.
6) Short side of 6 and long side of 8.
7) Short side of 1 and long side of 2
8) Both sides 10 (this is technically a square).
9) Short side of 6 and long side of 9.
10) Short side of 7 and long side of 8.
11) Short side of 2 and long side of 3.
12) Short side of 6 and long side of 9.
You can draw these a few different ways to still get a correct result, so above are just one way of doing it.
Mortgage collateral is the asset that secures the mortgage loan. Traditionally, the mortgage collateral is the asset the loan finances. If you fail to make payments to your lender on the loan, your lender has the option to claim ownership of the property due to its security interest.