Spins a fair spinner numbered 1 - 5 and flips a fair coin. What is the probability of obtaining a factor of 15 and a tail?

Answer: [tex]\dfrac{3}{10}[/tex]Step-by-step explanation:Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.The factors of 15 = [tex]1,\ 3,\ 5[/tex]Then ,the probability of obtaining a factor of 15 is given by :-[tex]P(A)=\dfrac{3}{5}[/tex]The probability of getting a tail :-[tex]P(B)=\dfrac{1}{2}[/tex]Since both the events are independent , thusThe probability of obtaining a factor of 15 and a tail is given by :-[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]Hence, the required probability : [tex]\dfrac{3}{10}[/tex]