Help me please i’m suck on this one!!

The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(

Umnica [9.8K]

Answer:

(a) $A_1$ and $A_2$ are indeed mutually-exclusive.

(b) $\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}$ , whereas $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

(c) $\displaystyle P(B) = \frac{9}{100}$ .

(d) $\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}$ , whereas $P(A_1 \; |\; B) = \displaystyle \frac{4}{9}$

Step-by-step explanation:

$P(A_1 \; \cap \; A_2) = 0$ means that it is impossible for events $A_1$ and $A_2$ to happen at the same time. Therefore, event $A_1$ and $A_2$ are mutually-exclusive.

By the definition of conditional probability:

$\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}$ .

Rearrange to obtain:

$\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}$ .

Similarly:

$\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}$ .

Note that:

$\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}$ .

In other words, $A_1$ and $A_2$ are collectively-exhaustive. Since $A_1$ and $A_2$ are collectively-exhaustive and mutually-exclusive at the same time:

$\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ .

By Bayes' Theorem:

$\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}$ .

Similarly:

$\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}$ .

6 0

3 years ago

Which of the following is equal to the expression below?

Solnce55 [7]

Answer:

choice c

Step-by-step explanation:

3 0

3 years ago

Percents

pentagon [3]

Answer:

$10.17
$70.57

Step-by-step explanation:

1. The change in value was 12.6% of $80.74, calculated as ...

0.126×$80.74 = $10.17324 ≈ $10.17

__

2. The new price is lower than the price yesterday by that amount, so is ...

$80.74 -10.17 = $70.57

_____

<em>Note on percents</em>

A percent should be no mystery. The word "per cent" literally means "per hundred", or "/100" in symbols. The symbol "%" is a shorthand way to write "/100". So 12.6% means 12.6/100 = 126/1000 = 0.126.

When written as a decimal, the units digit of a percent is placed in the hundredths digit of the decimal number, as you can see in the example above. (The "2" in "12.6" is in the hundredths place in 0.126.)

Generally percentages are used to express ratios. They are usually a "pure number" with no units attached. Since they are a ratio, they are generally useless unless you know what the numbers involved in the ratio are. Here, the denominator of the ratio, the "base" or "reference", is yesterday's stock price. The percentage is described as the drop in price since yesterday, so it is the ratio ...

<em>(drop in price since yesterday)/(yesterday's price)</em>

Both of these values have units of dollars, so the numerator units cancel the denominator units and what is left is a pure number. The ratio is 0.126, so to express it as a percentage, we multiply it by 100%. Of course, 100% = 100/100 = 1, so we haven't changed the value; we've only changed the way it is presented. That is ...

0.126 = 0.126 × 100% = 12.6%

_____

<em>Additional note on decimals and percents</em>

You may hear that to convert a decimal to a percent, you multiply it by 100. That is only partly right. Multiplying anything by 100 changes its value by that factor. When you change a decimal to a percentage, the goal is <em>not</em> to change the <em>value</em>, merely the <em>form</em>. What you actually want to do is multiply by 100% = 100/100. In the example we're using here, this looks like ...

0.126 × 100/100 = 12.6/100 = 12.6% . . . . . . remember that % means /100.

5 0

3 years ago

I need help with this

amid [387]

Answer:

x = 27

Step-by-step explanation:

this problem is similar to a scale drawing where we can set up a proportion:

'x' is to 5 as 162 is to 30

x/5 = 162/30

cross-multiply:

30x = 810

x = 810/30

x = 27

7 0

2 years ago

Read 2 more answers

Choose the answer that is equal to the expression below.<br> 5^2.5^0

sergiy2304 [10]

Answer:

<em>Any number(except maybe 0, do not play games with 0)) raised to 0 power is equal, so 5^2*1=25:</em>

3 0

4 years ago