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]
2 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]2 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
Subtraction of fractions 7 1/4 - 2 1/8 =
krek1111 [17]

Answer:

Exact form: 41/8

Decimal: 5.125

Mixed Fraction: 5 1/8

8 0
3 years ago
Read 2 more answers
Teachers of two history classes bought tickets to go on a field trip to a local museum. Mr. Lowe paid $115 for 4 adult tickets a
Papessa [141]
4a + 20s = 115
5a + 23s = 135.25
3 0
3 years ago
Read 2 more answers
Alexia used three teams of paper in her first semester of school. Each team has the same number of sheets. She used another 40 s
AysviL [449]
3x + 40, where x is the amount of sheets in each team 
6 0
3 years ago
Greg wants to buy four pieces of candy. They cost $1.37, $0.69, $0.89, and $1.15.
zloy xaker [14]

Answer:

$0.90

Step-by-step explanation:

5 - (1.37+.69+.89+1.15)

5-4.10 = .90

7 0
2 years ago
Read 2 more answers
A bag contains 4 red marbles, 16 yellow marbles, 5 purple, 16 blue marbles, and 10 green marbles. What is the probability of pul
Tasya [4]

red or green / total

4 + 10 / 4 +16 +5 +16 +10

14 / 51

8 0
3 years ago
Other questions:
  • Which of the following represents the most accurate estimation of 30-18
    12·1 answer
  • What is 2|u| – |v|, if u = –9 and v = –2? <br><br> A. –18<br> B. 16<br> C. –20<br> D. 20
    14·2 answers
  • How to make 12 and half to a percent
    8·1 answer
  • (1 pt) Lucas cut a board that is ft long and ft wide. What is the area of the board? Express your answer in simplest form. A. sq
    12·1 answer
  • An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. 1)
    14·1 answer
  • Find two natural numbers whose product<br> is 50 and whose sum is 27.
    6·1 answer
  • The sum of the reciprocal of a number and 3/5 is 7/10 find the number
    11·1 answer
  • PLEASE HELP I WILL GIVE 25 POINTS AND BRAINLIEST TO WHOEVER ANSWERS CORRECTLY! John is making baked goods for a party. He can ei
    12·1 answer
  • Can you help me solve this?<br><br> 6 ÷ 2(1+2) = ?
    15·1 answer
  • Hitung nilai x bagi persamaan <br>Calculate the value of x for the equation ​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!