Question

I need help,there is more to the question so I’ll send the rest when I get the tutor

Answer 1

From the information provided, the diagram would appear as follows;

The sample space of the spinner i;

`S=\mleft\lbrace1,2,3,4,5,6,7\mright\rbrace`

(2) What is set A?

`A=\mleft\lbrace4,5,6,7\mright\rbrace`

(3) What is the probability of spinning a number greater than or equal to 4.

`\begin{gathered} P\lbrack x\ge4\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}} \\ P\lbrack x\ge4\rbrack=(4)/(7) \end{gathered}`

(4) What is set B?

`B=\mleft\lbrace1,3,5,7\mright\rbrace`

(6) What is A and B?

`\begin{gathered} A=\mleft\lbrace4,5,6,7\mright\rbrace \\ B=\mleft\lbrace1,3,5,7\mright\rbrace \\ A\text{ and B=}\mleft\lbrace1,3,4,5,6,7\mright\rbrace \end{gathered}`

(5) What is the probability of spinning an odd number?

`\begin{gathered} P\lbrack\text{Odd number\rbrack=}\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}} \\ P\lbrack\text{Odd number\rbrack=}(4)/(7) \end{gathered}`

(7) What is the probability of spinning a number greater than or equal to 4 and odd?

`\begin{gathered} P\lbrack A\text{ and B\rbrack=P\lbrack{}A\rbrack x P\lbrack{}B\rbrack} \\ P\lbrack A\text{ and B\rbrack=}(4)/(7)*(4)/(7) \\ P\lbrack A\text{ and B\rbrack=}(16)/(49) \end{gathered}`

(8) What is the probability of spinning a number NOT greater than or equal to 4

or an odd number?

`\begin{gathered} P\lbrack A^(\prime)\rbrack=1-P\lbrack A\rbrack \\ P\lbrack A^(\prime)\rbrack=1-(4)/(7) \\ P\lbrack A^(\prime)\rbrack=(3)/(7) \end{gathered}`
`P\lbrack Odd\text{\rbrack=}(4)/(7)`

Therefore;

`\begin{gathered} P\lbrack A^(\prime)\text{ OR Odd\rbrack=P\lbrack{}A'\rbrack+P\lbrack{}Odd\rbrack} \\ P\lbrack A^(\prime)\text{ OR Odd\rbrack=}(3)/(7)+(4)/(7) \\ P\lbrack A^(\prime)\text{ OR Odd\rbrack=}(3+4)/(7) \\ P\lbrack A^(\prime)\text{ OR Odd\rbrack=}(7)/(7) \\ P\lbrack A^(\prime)\text{ OR Odd\rbrack=1} \end{gathered}`