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.

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

(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?

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

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

$\begin{gathered} P\lbrack A\text{ and B\rbrack=P\lbrack{}A\rbrack x P\lbrack{}B\rbrack} \\ P\lbrack A\text{ and B\rbrack=}\frac{4}{7}\times\frac{4}{7} \\ P\lbrack A\text{ and B\rbrack=}\frac{16}{49} \end{gathered}$

(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-\frac{4}{7} \\ P\lbrack A^{\prime}\rbrack=\frac{3}{7} \end{gathered}$$P\lbrack Odd\text{\rbrack=}\frac{4}{7}$

Therefore;

$\begin{gathered} P\lbrack A^{\prime}\text{ OR Odd\rbrack=P\lbrack{}A'\rbrack+P\lbrack{}Odd\rbrack} \\ P\lbrack A^{\prime}\text{ OR Odd\rbrack=}\frac{3}{7}+\frac{4}{7} \\ P\lbrack A^{\prime}\text{ OR Odd\rbrack=}\frac{3+4}{7} \\ P\lbrack A^{\prime}\text{ OR Odd\rbrack=}\frac{7}{7} \\ P\lbrack A^{\prime}\text{ OR Odd\rbrack=1} \end{gathered}$