1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
myrzilka [38]
3 years ago
5

Two professors are applying for grants. Professor Jane has a probability of 0.61 of being funded. Professor Joe has probability

0.27 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded? Give your answer to four decimal places. 0.1647 Correct: Your answer is correct. b. What is the probability that at least one of the professors will be funded? Give your answer to four decimal places. .7153 Correct: Your answer is correct. c. What is the probability that Professor Jane is funded but Professor Joe is not? Give your answer to four decimal places.
Mathematics
1 answer:
Anna11 [10]3 years ago
4 0

Answer:

  • a. 0.1647;
  • b. 0.7153;
  • c. 0.4453.

Step-by-step explanation:

By definition, if two event A and B are independent, then

P(A\cap B) = P(A) \cdot P(B). (P(A\cap B) is the probability that the outcome of both event A and event B are true.)

<h3>a.</h3>

Since the outcome of these two events are independent,

\begin{aligned}P(\texttt{Jane} \cap \texttt{Joe}) &= P(\texttt{Jane}) \cdot P(\texttt{Joe})\\ &= 0.61 \times 0.27 \\&= 0.1647\end{aligned}.

<h3>b.</h3>

The logic not operator \lnot or the prime superscript ^{\prime} denotes that an event does not happen.  

P(\texttt{Jane}^{\prime}) = 1 - P(\texttt{Jane}) = 1- 0.61 = 0.39.

P(\texttt{Joe}^{\prime}) = 1 - P(\texttt{Joe}) = 1- 0.27 = 0.73.

Since the two events \texttt{Jane} and \texttt{Joe}, \texttt{Jane}^{\prime} and \texttt{Joe}^{\prime} are also independent. Probability that neither professor got funded:

P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = P(\texttt{Jane}^{\prime}) \cdot P(\texttt{Joe}^{\prime}) = 0.39 \times 0.73 = 0.2847.

Probability that at least one professor got funded- in other words, it is not true that neither professor got funded:

P((\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime})^{\prime}) = 1- P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = 0.7153.

<h3>c.</h3>

Similarly, since the two events \texttt{Jane} and \texttt{Joe}, \texttt{Jane} and \texttt{Joe}^{\prime} are also independent. Probability that Jane but not Joe got funded:

P(\texttt{Jane} \cap (\texttt{Joe}^{\prime})) = P(\texttt{Jane}) \cdot P(\texttt{Joe}^{\prime}) = 0.61 \times 0.73 = 0.4453.

You might be interested in
I need help i'm about to cry lol
grigory [225]

Answer and Step-by-step explanation:

The answer is the last answer choice.

g(x) = -(x + 2)^2 + 1

We don't even have to look at the numbers to tell that this is the correct answer. We look at what is being placed there.

The equation for a transformed function is:

f(x) = a(x-h)^2 + k

a determines the scale of the graph and whether the graph opens up or down.

h determines whether the graph shifts left or right.

k determines whether the graph shifts up or down.

We see that there is a -1 for a, which means the graph will be facing downwards. We see a 2 for where h is, but it really is a -2, and when it becomes a positive after simplifying, the graph will shift to the left.

k is a positive 1, so the graph will be shifted up 1 unit.

<u>Thus, the answer is the last answer choice.</u>

<u></u>

<u></u>

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

5 0
3 years ago
Read 2 more answers
The mass of a ball is 128 g. It has a density of 0.5 g/cm³.
liraira [26]

Answer:

The volume of the ball is 256 cm³

Step-by-step explanation:

we know that

The density is equal to the ratio of the mass by the volume

D=m/V

Solve for V

The volume is equal to the ratio of the mass by the density

V=m/D

In this problem we have

m=128 g

D=0.5 g/cm³

substitute

V=128/0.5=256 cm³

7 0
4 years ago
The manager of a large grocery store wants to inspect an incoming shipment of oranges to determine the
Nimfa-mama [501]

Answer:

b

Step-by-step explanation:

The variability of the proportion of blemishes for Mary's sample will be greater than the variability of Pat's.

7 0
3 years ago
F(x) = -x + 5, what is the value of f(-4)?<br> I
liberstina [14]

Answer:

Step-by-step explanation:

F(x)=-x+5

So

f(-4)= -(-4)+5

f(-4)= 4+5

f(-4)= 8

Only we have to substitute value of x then after simplification we will get answer..Hope this will help

7 0
3 years ago
Read 2 more answers
Factor completely and check mentally. 18x^2yz+12xy^2z+6xyz^2
amm1812
6xyz(3x+2y+z...................
7 0
3 years ago
Read 2 more answers
Other questions:
  • School calculators are sold by one company only in packages of 11 and packages of 15. What is the largest number of calculators
    8·1 answer
  • How far can person run in 15 minutes if he or she runs at an average speed of 0.15/min
    8·1 answer
  • Janice read 280 words in 7 minutes. How many words could she read in one minute?
    15·1 answer
  • Find the equation of the line in y=mx+b form with slope 3 that passes through the point (5,19)
    10·1 answer
  • How can you use regrouping to solve the equation 32-5 =
    15·2 answers
  • Which fraction is equivalent to 3<br> 1/3<br> 2/1<br> 3/3<br> 5/2<br> 6/2
    7·1 answer
  • 3(3v-5) = 39 <br>Simplify your answer as much as possible.<br><br>​
    15·2 answers
  • You need to reserve a shelter at the park. You expect that it will take 1 3/4
    11·1 answer
  • Can you guys work it out
    14·2 answers
  • Solve for a<br> (log(a-1))^2 =log10
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!