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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.

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Given:

(a+10) and (a+20) are supplementary

To find:

Each angle

Steps:

if 2 angles are supplementary that means they add up to 180°

(a + 10) + (a + 20) = 180

   a + 10 + a + 20 = 180

              2a + 30 = 180

                      2a = 180 - 30

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Multiply each equation by a constant that would help to eliminate the y terms.
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Answer:

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

Step-by-step explanation:

Given:

2x-5y=-21         ......................Equation ( 1 )

3x-3y=-18         ......................Equation ( 2 )

To Find:

Expression after multiplying to eliminate y term,

Solution:

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so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,

Therefore the required resulting equation is

6x-15y=-63\\-15x+15y=90

6 x minus 15 y = negative 63.

Negative 15 x + 15 y = 90

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