Ask question

Ask question

All categories

17 days ago

13

Imagine you are a financial analyst at an investment bank. According to your research of publicly-traded companies, 60% of the c

ompanies that increased their share price by more than 5% in the last three years replaced their CEOs during the period. At the same time, only 35% of the companies that did not increase their share price by more than 5% in the same period replaced their CEOs. Knowing that the probability that the stock prices grow by more than 5% is 4%, find the probability that the shares of a company that fires its CEO will increase by more than 5%.

1 answer:

lawyer [9.2K]17 days ago

5 0

Answer:

0.0667 represents a 6.67% likelihood that the stock of a firm that dismisses its CEO will rise by over 5%.

Step-by-step explanation:

Conditional Probability

To answer this question, we apply the conditional probability formula, which is

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

In this formula,

P(B|A) denotes the chance of event B occurring provided that A occurred.

$P(A \cap B)$ represents the probability of both A and B occurring.

P(A) indicates the likelihood of A occurring.

In this scenario:

Event A: The company dismisses the CEO.

Event B: The shares surge by more than 5%.

Probability of a company dismissing its CEO:

35% of 100 - 4 = 96% (indicating shares did not rise by over 5%).

60% of 4% (indicating shares indeed rose by more than 5%).

<ptherefore>

$P(A) = 0.35*0.96 + 0.6*0.04 = 0.36$

Overlap of events A and B:

The scenario where a CEO is fired and shares increase by more than 5% occurs 60% of the time in a 4% chance. So,

$P(A \cap B) = 0.6*0.04 = 0.024$

The likelihood of shares increasing by more than 5% after a CEO is dismissed.

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.024}{0.36} = 0.0667$

0.0667 translates to a 6.67% probability that shares from a company firing its CEO will see a rise exceeding 5%.

</ptherefore>

You might be interested in

Allan is ordering a set of rational numbers that includes positive values, negative values, fractions, and decimal numbers. How

Inessa [9006]

Arrange them starting from the smallest to the largest.

7 0

1 month ago

Read 3 more answers

Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer) between a "worker" com

Inessa [9006]

Answer:

a. Alpha equals 3.014 while beta equals 12.442

b. The likelihood that the data transfer duration surpasses 50ms is 0.238

c. The chance that data transfer time falls between 50 and 75 ms is 0.176

Step-by-step explanation:

a. Given the data, the mean and standard deviation for the random variable X are 37.5 ms and 21.6, respectively.

Thus, E(X)=37.5 and V(X)=(21.6)∧2

To find alpha, we need to apply the formula:

alpha=E(X)∧2/V(X)

alpha=(37.5)∧2/21.6∧2

alpha=1,406.25 /466.56

alpha=3.014

To determine beta, the following formula is employed:

β= V(X) ∧2/E(X)

β=(21.6) ∧2/37.5

β=466.56 /37.5

β=12.442

b. With E(X)=37.5 and V(X)=(21.6)∧2,

Hence, P(X>50)=1−P(X≤50)

To find the probability of data transfer time exceeding 50ms, we use the formula:

P(X>50)=1−P(X≤50)

=1−0.762

=0.238

The chance of data transfer time exceeding 50ms is 0.238

c. With E(X)=37.5 and V(X)=(21.6)∧2,

Thus, P(50<X<75)=P(X<75)−P(X<50)

To find the probability that data transfer time is between 50 and 75 ms, we apply the formula:

P(50<X<75)=P(X<75)−P(X<50)

=0.938−0.762

=0.176

The probability that data transfer time falls between 50 and 75 ms is 0.176

6 0

12 days ago

The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −20 3x

PIT_PIT [9121]

The correct choice is option D. The given equations are:...[1]...[2] Multiply equation [1] by 5 on both sides; we have...[3]. By using the elimination method, we can add equations [2] and [3] to eliminate y and determine x, resulting in... Dividing both sides by 13 yields x = 3. Substituting x back into equation [1] results in 2(3) - y = -4, which simplifies to 6 - y = -4. After subtracting 6 from both sides, we find -y = -10. Dividing through by -1 gives y = 10. Hence, the solution is (3, 10). Consequently, a valid equation that can replace 3x + 5y = 59 in the original set while still yielding the same result is 13x = 39.

6 0

9 days ago

Read 2 more answers

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town

Leona [9271]

Answer:

In my opinion, it's fitting to offer assistance.

Step-by-step explanation:

3 0

16 days ago

Read 2 more answers

Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at

Svet_ta [9518]

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by $x(t)$ in grams, is defined by the differential equation,

$x'(t)=15-\dfrac{3x(t)}{10}$

which is linear. Shift the $x$ term to the right side, then multiply both sides by $e^{3t/10}$ :

$e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}$

$\implies\left(e^{3t/10}x\right)'=15e^{3t/10}$

Next, integrate both sides and solve for $x$ :

$e^{3t/10}x=50e^{3t/10}+C$

$\implies x(t)=50+Ce^{-3t/10}$

Initially, the tank contains 5 g of salt at time $t=0$ , so we have

$5=50+C\implies C=-45$

$\implies\boxed{x(t)=50-45e^{-3t/10}}$

The duration required for the tank to contain 20 g of salt is $t$ , such that

$20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}$

3 0

1 month ago