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
zimovet [89]
3 years ago
9

Two number cubes are rolled for two separate events: Event A is the event that the sum of the numbers on both cubes is less than

10.
Event B is the event that the sum of the numbers on both cubes is a multiple of 3.
Complete the conditional probability for event B given that event A occurs first by writing A and B in the blanks:

Mathematics
1 answer:
Agata [3.3K]3 years ago
6 0

Let us first make the sample space for the event A. The Sample Space will be:


(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)


(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)


(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)


(4,1) (4,2) (4,3) (4,4) (4,5)


(5,1) (5,2) (5,3) (5,4)


(6,1) (6,2) (6,3)


As can be clearly seen the Sample Space for the event A has 30 elements in it.


Now, it is given in the question that the event A has already occurred and we need to find the probability of the event B occurring given that the event A has already occurred.


Now, as we can see, from the sample space, only 11 events out of the 30 are the events of interest to us. This is shown in bold below:


(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)


(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)


(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)


(4,1) (4,2) (4,3) (4,4) (4,5)


(5,1) (5,2) (5,3) (5,4)


(6,1) (6,2) (6,3)


Thus, the probability that the event B occurs given that the event A has already occurred is:




In percentage the required probability is 36.7% approximately.

You might be interested in
A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0
3 years ago
how many such tests would it take for the probability of committing at least one type i error to be at least 0.7? (round your an
drek231 [11]

The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118   .

In the question ,

it is given that ,

the probability of committing at least , type I error is = 0.7

we  have to find the number of tests ,

let the number of test be n ,

the above mentioned situation can be written as

1 - P(no type I error is committed) ≥ P(at least type I error is committed)

which is written as ,

1 - (1 - 0.01)ⁿ ≥ 0.7

-(0.99)ⁿ ≥ 0.7 - 1

(0.99)ⁿ ≤ 0.3

On further simplification ,

we get ,

n ≈ 118 .

Therefore , the number of tests are 118 .

Learn more about Error here

brainly.com/question/17062640

#SPJ4

4 0
1 year ago
A foreign tourist went shopping in a shop in Hungary with only euros. Luckily for him, the shop accepted euros. At the end of th
erik [133]

Answer:

you got back with 3,050

Step-by-step explanation:

multiplied 305 by 10

3 0
2 years ago
Read 2 more answers
7. If the value of x varies directly with the value of y, and x = 3 when y = 21. What is the valu
konstantin123 [22]

Answer:

15

Step-by-step explanation:

Because x=y÷7

i.e,105÷7=15

3 0
3 years ago
Read 2 more answers
Tickets to a 3D movie cost $13 for an adult and $6 for each child. Let C represent the number of children's tickets and A repres
ch4aika [34]
You multiply... 46*13= 598 then multiply 20*6= 120 add them 598+120=$718
13a+6c=$ hope this helped you have a great rest of the day!!
5 0
3 years ago
Other questions:
  • Write 12/15 in the simplest form
    5·2 answers
  • Charlie runs at a speed of 3 yd./s about how many miles per hour does Charlie run
    6·1 answer
  • I WILL GIVE BRAINLIEST TO THE FIRST PERSON!A spinner has 8 equal-sized sections. The probability that the spinner will stop abov
    13·2 answers
  • Here are two steps from the derivation of the quadratic formula. What room place between the first step and the second step?
    10·2 answers
  • A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed?
    5·2 answers
  • Last question of the day!!
    6·1 answer
  • If the mean of x and 4x is 10, the x = ?
    8·2 answers
  • -5x+2y=6<br> -x+2y=-2 <br> what is the solution to the system of equations?
    15·1 answer
  • Use the multiplier method to increase £258 by 43
    6·1 answer
  • 1.4.3 Quiz: Linear Equations And Inequalities
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!