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Otrada [13]
3 years ago
11

Suppose that A and B are two events in a sample space, S, which are independent and which have equal probability, p, of occurrin

g. Suppose further that the probability that neither A nor B occurs is 0.81. Find the probability that both A and B occur.
Mathematics
1 answer:
pychu [463]3 years ago
7 0

Answer:

The probability that both A and B occur is P = 0.01

Step-by-step explanation:

Both events A and B have a probability p of occurring.

Then both events A and B have a probability (1 - p) of NOT occurring.

The probability that neither A or B occurs is equal to the product of the individual probabilities, and this is equal to 0.81, then:

(1 - p)*(1 - p) = 0.81

1 - 2*p + p^2 = 0.81

p^2 - 2*p + 0.19 = 0

We can solve this if we use Bhaskara's equation, the two solutions are:

p = \frac{-(-2) +- \sqrt{(-2)^2 - 4*1*0.19} }{2*1}  = \frac{2 + - 1.8}{2}

Then the two solutions are:

p = (2 + 1.8)/2 = 3.8/2 = 1.9

A probability must be a number between zero and one, and this is larger than one, so this solution can be discarded.

the other solution is:

p = (2 - 1.8)/2 = 0.2/2 = 0.1

This means that the probability that event A occurs is p = 0.1

And the probability that event B occurs is p = 0.1

The probability that both events occur is equal to the product of the individual probabilities, which is:

P = 0.1*0.1 = 0.01

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4.b.

Answer:  See below.

Step-by-step explanation:

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<u>f(-11) = -22</u>

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<u></u>

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4.a.  f(7) = 5(7)+50

<u>f(7) = 85</u>

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Continue in the same fashion for these types of problems.

7 0
2 years ago
A bank features a savings account that has an annual percentage rate of 3.5% with interest compounded quarterly. Vanessa deposit
vazorg [7]

Answer:

APY = 0.04 or 4%

Step-by-step explanation:

Given the annual percentage rate of 3.5% that is compounded quarterly, and a principal of $6,500:

We can use the following formula to solve for the annual percentage yield (APY):

APY =  (1 + \frac{r}{n})^n - 1

where <em>r</em> = interest rate = 3.5% or 0.035

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We can plug in the values into the equation:

APY =  (1 + \frac{r}{n})^n - 1

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8 0
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Answer:

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6 0
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