Answer: Probability of obtaining a multiple of 3 and a factor of 10 is given by
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Since we have given that
There is a fair spinner numbered 1-5 and a fair dice
Total number of outcomes of fair spinner = 5
Total number of outcomes of a fair dice = 6
Let Event A: Getting a multiple of 3 on a spinner
Event B: Getting a factor of 10 on a fair dice
The possible outcomes of multiple of 3 on a spinner is
[tex]3[/tex]
The possible outcomes of factor of 10 on a fair dice are
[tex]1,2,5[/tex]
So,
[tex]P(A)=\frac{1}{5}[/tex]
and
[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]
Since A and B are independent events so,
[tex]P(A\ and\ B)=P(A).P(B)\\\\P(A\ and\ B)=\frac{1}{5}\times \frac{1}{2}\\\\P(A\ and\ B)=\frac{1}{10}[/tex]
Hence, Probability of obtaining a multiple of 3 and a factor of 10 is given by
[tex]\frac{1}{10}[/tex]
