Roll a die and consider the following two events={2, 3, 6}, event ={1, 5, 6}. Are the events E and F independent?Choose the correct answer below.- No, because the probability of F occurring is higher if it is known that E has occurred.- No, because there is at least one roll which leads to both E and F occurring.- Yes, because the probability of F occurring is higher if it is known that E has occurred.- Yes, because each roll of the die is an independent event.

Answer:Option 1 - No, the probability of F occurring is higher if it is known that E has occurred.Step-by-step explanation:Given : Roll a die and consider the following two events={2, 3, 6}, event ={1, 5, 6}. To find : Are the events E and F independent?Solution : E={2, 3, 6}, F={1, 5, 6}They are not independent event as 6 is common in both the events.Now, verifying by applying independent property,Probability of event E is [tex]P(E)=\frac{3}{6}=\frac{1}{2}[/tex]Probability of event F is [tex]P(F)=\frac{3}{6}=\frac{1}{2}[/tex]Probability of E and F is [tex]P(E\cap F)=\frac{1}{6}[/tex]Probability of F occuring when it is known that e has occured.i.e. [tex]P(F/E)=\frac{P(E\cap F)}{P(E)}[/tex] [tex]P(F/E)=\frac{\frac{1}{6}}{\frac{1}{2}}[/tex][tex]P(F/E)=\frac{1}{3}[/tex][tex]P(F)>P(F/E)[/tex]i.e. The probability of F occurring is higher if it is known that E has occurred.Therefore, The correct option is 1.Events E and F are not independent, because  the probability of F occurring is higher if it is known that E has occurred.