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A consumer products company found that 42% of successful products also received favorable results from test market research, w

blagie [28]

Answer:

(1) The probability of a successful product given the product is favorable is 0.7778.

(2) The probability of a successful product given the product is unfavorable is 0.2391.

(3) The probability of a unsuccessful product given the product is favorable is 0.2222.

(4) The probability of a unsuccessful product given the product is favorable is 0.7609.

Step-by-step explanation:

Denote the events as follows:

S = a product is successful.

F = a product is favorable.

The information provided is:

$P(S\cap F)=0.42\\P(S\cap F^{c})=0.11\\P(S^{c}\cap F)=0.12\\P(S^{c}\cap F^{c})=0.35\\$

The law of total probability states that:

$P(A)=P(A\cap B)+P(A\cap B^{c})$

Use the law of total probability to compute the probability of a favorable product as follows:

$P(F)=P(S\cap F)+P(S^{c}\cap F)\\=0.42+0.12\\=0.54$

The probability of a favorable product is 0.54.

The conditional probability of an event A given that another event B has already occurred is:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

(1)

Compute the value of P (S|F) as follows:

$P(S|F)=\frac{P(S\cap F)}{P(F)}=\frac{0.42}{0.54}=0.7778$

Thus, the probability of a successful product given the product is favorable is 0.7778.

(2)

Compute the value of $P(S|F^{c})$ as follows:

$P(S|F^{c})=\frac{P(S\cap F^{c})}{P(F^{c})}=\frac{0.11}{(1-0.54)}=0.2391$

Thus, the probability of a successful product given the product is unfavorable is 0.2391.

(3)

Compute the value of $P (S^{c}|F)$ as follows:

$P (S^{c}|F)=\frac{P(S^{c}\cap F)}{P(F)}=\frac{0.12}{0.54}=0.2222$

Thus, the probability of a unsuccessful product given the product is favorable is 0.2222.

(4)

Compute the value of $P (S^{c}|F^{c})$ as follows:

$P (S^{c}|F)=\frac{P(S^{c}\cap F^{c})}{P(F^{c})}=\frac{0.35}{(1-0.54)}=0.7609$

Thus, the probability of a unsuccessful product given the product is favorable is 0.7609.

8 0

3 years ago

Can two equilateral triangles always be congrunet ? give resons

erastova [34]

SOLUTION :

YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,

& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).

________________________________

MARK BRAINLIEST!

8 0

2 years ago

A fun noodle is 1.31 meters long. What is it's length in inches, if 1 inch = 0.0254 meters?

Genrish500 [490]

.033274
hope it helps

4 0

3 years ago

If f(x) and g(x) are inverse functions of each other, Which of the following shows the graph of f(g(x))

ella [17]

Answer:

The graph is attached; it is the graph of f(x) = x.

Step-by-step explanation:

Two functions are inverses if their composites form the function f(x) = x.

Take, for example, the function f(x) = 2x-4. We can write this as y=2x-4.

To find the inverse, we isolate x. To do this, first add 4 to each side:

y+4 = 2x-4+4

y+4 = 2x

Divide both sides by 2:

(y+4)/2 = 2x/2

y/2 + 4/2 = x

1/2y + 2 = x

Swap x and y, and the inverse is

y=1/2x+2

This can be written as g(x).

The composite of these two functions, f(g(x)), is:

f(1/2x+2) = 2(1/2x+2)-4

= 2(1/2x)+2(2)-4

=1x+4-4

= x

The composite of two functions is always f(x) = x.

This means the graph will have a slope of 1 and a y-intercept of 0.

4 0

3 years ago

Read 2 more answers

When 1,250 Superscript three-fourths is written in simplest radical form, which value remains under the radical?

Dvinal [7]

The value remains under the radical is 8 ⇒ last answer

Step-by-step explanation:

Let us revise how to write the exponent as a radical

$a^{\frac{m}{n}}$ can be written as $\sqrt[n]{a^{m}}$
To simplify the radical factorize the base "a" to its prime factors

Example:

$(54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}$ ,
Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 = $2(3)^{3}$
$\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}$
2² can not go out the radical because 2 is less than 3 not divisible by 3
$3^{6}$ can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical
$\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}$