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Alex
3 years ago
6

2.4 Backgammon. Backgammon is a board game for two players in which the playing pieces are moved according to the roll of two di

ce. Players win by removing all of their pieces from the board, so it is usually good to roll high numbers. You are playing backgammon with a friend and you roll two 6s in your first roll and two 6s in your second roll. Your friend rolls two 3s in his first roll and again in his second row. Your friend claims that you are cheating, because rolling double 6s twice in a row is very unlikely. Using probability, show that your rolls were just as likely as his.
Mathematics
1 answer:
muminat3 years ago
7 0

Answer:

The claim is not fair because:

  • Probability of roliing two 6s = Probability of rolling two 3s = 1/36

Step-by-step explanation:

The <em>probaility</em> of an event is defined as the number of favorable outcomes divided by the number of total possible events.

P (event E) = number of outcomes for event E / number of possible events

1. <u>As </u><u>first step</u><u>, you may draw a table to find the </u><u>sample space</u><u> (set of all possible outcomes)</u>.

<u>Sample space</u>

The results of the rolling two dice are summarized in this table:

                    Second roll    1       2       3       4        5      6

First roll

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

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

  3                                     (3,1)  (3,2)  <u>(3,3)</u>   (3,4)  (3,5)  (3,6)

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

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

  6                                     (6,1)  (6,2)  (6,3)  (6,4)  (6,5)  <u>(6,6)</u>

<u></u>

2.<u>Now, in that table, you can observe</u>:

The results (3,3) and (6,6) are highlited.

a) Total number of events: 6 × 6 = 36

b) Nnmber of outcomes for the event rolling two 6s (6,6): 1

c) Number of outcomes for the event rolling two 3s (3,3): 1

3) <u>Next, you can calculate the probabilities:</u>

a) Probability rolling two 6s = 1 / 36

b) Probability of rolling two 3s: 1 / 36

4. <u>Conclusion</u>: the probabilities prove that rolling two 6s is just as likely as rolling two 3s.

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Mark and don are planning to sell each of their marble collections at a garage sale. if don has 4 more than 5 times the number o
natita [175]

Mark and Don have to sell 11 and 59 marbles respectively.

<em><u>Explanation</u></em>

Lets assume, the number of marbles Mark has  is x

As, Don has 4 more than 5 times the number of marbles mark has, so the number of marbles Don has = 5x+ 4

Question says that the total number of marbles is 70. So, the equation will be...

x+(5x+4)= 70\\ \\ 6x+4= 70 \\ \\ 6x = 70-4\\ \\ 6x=66 \\ \\ x= \frac{66}{6}= 11

<em>So, the number of marbles Mark has = 11 </em>

<em>and the number of marbles Don has = (5*11)+4 = 55+4= 59</em>

6 0
3 years ago
1.2.71
egoroff_w [7]

Answer:

Step-by-step explanation:

Set up an equation, where x is the number of gallons of 60% antifreeze solution.

Represent the percentages of antifreeze with decimal values.

0.6x + 0.3(80) = 0.5(x + 80)

Simplify and solve for x:

0.6x + 24 = 0.5x + 40

0.1x = 16

x = 160

So, you have to mix 160 gallons of a 60% antifreeze solution

6 0
3 years ago
I rlly need help help me out pls
rusak2 [61]

Answer:

San francisco

Step-by-step explanation:

once you divide the distance by time then multiply the answer by the longest amount of time (aka 4)

San francisco = 2556

Minot = 1826

Phoenix = 2252

6 0
2 years ago
Which data set is the most spread from its mean?
spin [16.1K]

Option B (22,16,18,36)

Mean- Mean is an average of the data collected in the data set. It can be found by dividing the sum of the values by the number of values. Median is the middle value of the data set when the values are placed in order from least to greatest.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

Add all the numbers (22+16+18+36) = 92

Avarage = sum of the all given numbers/ total numbers

total numbers =4

so avarage= mean= 92/4 =23

(22,16,18,36) has the most spread because one number as low as 16 and one as high as 36. Our mean is 23, so that means that the spread is huge.

Hence the answer is (22,16,18,36).

For more information about Mean

visit : brainly.com/question/1635504

#SPJ9

7 0
1 year ago
Carter lives on a street where all the house numbers are a multiple of 6. Name two house numbers between 601 and 650
GarryVolchara [31]

Answer:

606 and 612

Step-by-step explanation:

A number is a multiple of 6 if:

1. the sum of its integers can be divided by 3

2. The number is even (ending in 0, 2, 4, 6, 8

With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.

606:

6 is even

6 + 6 = 12

12 divided by 4 is 3

612:

2 is even

6 + 1 +  2=  9

9 divided by 3 is 3

7 0
3 years ago
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