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
kati45 [8]
3 years ago
10

An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.

Draw the possibility diagram of the product of the two numbers appearing on the die in each throw Use the possibility diagram to calculate the probability that the product of the two numbers is A prime number Not a perfect square A multiple of 5 Less than or equal to 21 Divisible by 4 or 6
Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
8 0

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]

<u>PART A</u>

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64

<u>PART B</u>

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

=\dfrac{15}{64}\\=0.234375

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625

You might be interested in
A ceramic vase that cost an antique store $5 was marked $20. What is the percentage markup on the price of the ceramic vase?
Anika [276]
The answer would be 75%%%%
8 0
3 years ago
Sarah runs a day camp in the summer and needs to buy paper towels and soap for the restrooms. She spends $129 on t cases of pape
Cloud [144]
Let x be the number of cases of paper towels and y be the number of cases of soap. The system of linear equation that would best represent the given is,
                                 x + y = 10
                               12x + 15y = 129
The values of x and y are 7 and 3. 

Sarah both 7 cases of paper towel.

It is not possible for Sarah to buy exactly 20 bottles because first of all the cases contains only 12 bottles and 20 is not divisible by 12. 
3 0
3 years ago
in an election for sheriff 210 people voted if there where 1260 possible voters write a ratio to compare the number of people wh
ale4655 [162]
210:1260

If simplified it is

1:6

If Hope this helped if any question feel free to ask!! :D

6 0
3 years ago
Where do you get the 2/5 and 3/5 from
-Dominant- [34]

Answer:

we can get 3/2 as the answer

5 0
2 years ago
If AD and BD are bisectors of CAB and CBA respectively. Find the sum of angles x and y.
olchik [2.2K]
The picture in the attached figure

step 1
we know that
It is given that AD and BD are bisectors of ∠CAB and ∠CBA respectively.
Therefore,
x = ∠CAB/2 -----> equation 1
y = ∠CBA/2 -----> equation 2

step 2
In triangle ABC,
∠CAB + ∠CBA + ∠ACB = 180° ----> [The sum of all three angles of a triangle is 180°]
∠CAB + ∠CBA + 110° = 180°
∠CAB + ∠CBA = 180° - 110°
∠CAB + ∠CBA = 70° ------> divide by 2 both sides
∠CAB/2 + ∠CBA/2 = 70/2 -------> equation 3
substitute equation 1 and equation 2 in equation 3
x+y=35

hence

the answer is
x+y =35°
⇒ x + y = 35° ...[From equation (1) and (2)]

5 0
3 years ago
Other questions:
  • (04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area
    10·1 answer
  • What is the distance TX?
    9·1 answer
  • Can someone please explain how i can solve this ...thank you very much
    8·2 answers
  • Tina has 3/5 pound erase she will use 2/3 of it to make fried rice for her family how much rice with Tina used to make fried ric
    6·2 answers
  • For the function given​ below, find a formula for the Riemann sum obtained by dividing the interval​ [a,b] into n equal subinter
    13·1 answer
  • A set of Megasus Horserunners is 159 euros. At an exchange rate of 1 euro = 1.16 dollars, what’s that in U.S dollars?
    10·1 answer
  • Which inequality is shown in the graph?
    12·1 answer
  • What is the ratio of 420m to 1 km
    13·2 answers
  • HELP ILL GIVE BRAINLIEST
    5·1 answer
  • Line segment AB has a length of 4 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!