Respuesta :
Answer:
Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
Step-by-step explanation:
We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.
And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.
Let the Probability that pointer will stop on an odd number = P(A)
Probability that pointer will stop on a number greater than 5 = P(B)
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]P(A\bigcap B)[/tex]
Probability that pointer will stop on an odd number or on a number greater than 5 = [tex]P(A\bigcup B)[/tex]
Here, Odd numbers = {1, 3, 5, 7} = 4
Numbers greater than 5 = {6, 7, 8} = 3
Also, Number which is odd and also greater than 5 = {7} = 1
Total numbers = 8
Now, Probability that pointer will stop on an odd number = [tex]\frac{4}{8}[/tex] = 0.5
Probability that pointer will stop on a number greater than 5 = [tex]\frac{3}{8}[/tex] = 0.375
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]\frac{1}{8}[/tex] = 0.125
Now, [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]
= 0.5 + 0.375 - 0.125
= 0.75
Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
The probability that the pointer will stop on an odd number or a number greater than 5 is 3/4
The sample space is:
[tex]\mathbf{S = \{1,2,3,4,5,6,7,8\}}[/tex]
Count = 8
The odd numbers are:
[tex]\mathbf{Odd = \{1,3,5,7\}}[/tex]
Count = 4
The probability of odd is:
[tex]\mathbf{P(odd) = \frac{4}{8} }[/tex]
The numbers greater than 5 are:
[tex]\mathbf{Greater= \{6,7,8\}}[/tex]
Count = 3
The probability of numbers greater than 5 is:
[tex]\mathbf{P(Greater) = \frac{3}{8}}[/tex]
Odd numbers greater than 5 are:
[tex]\mathbf{OddGreater= \{7\}}[/tex]
Count =1
The probability of odd numbers greater than 5 is:
[tex]\mathbf{P(OddGreater) = \frac{1}{8}}[/tex]
So, the probability that the pointer will stop on an odd number or a number greater than 5 is:
[tex]\mathbf{Pr = P(Odd) + P(Greater) - P(OddGreater)}[/tex]
This gives
[tex]\mathbf{Pr = \frac 48 + \frac 38 - \frac 18}[/tex]
[tex]\mathbf{Pr = \frac 68}[/tex]
Simplify
[tex]\mathbf{Pr = \frac 34}[/tex]
Hence, the required probability is 3/4
Read more about probabilities at:
https://brainly.com/question/11234923
