Answer: a) i. Yes
b) [tex]\dfrac{1}{36}[/tex]
c) [tex]\dfrac{1}{36}[/tex]
d) [tex]\dfrac{1}{18}[/tex]
Step-by-step explanation:
a) If we roll two different dice , then the outcomes on the dice are independent of each other.
So , if we roll two fair dice, one green and one red. , then the outcomes on the dice are independent.
Therefore , correct answer is "Yes".
b) Total outcomes on each die = 6 (1,2,3,4,5,6)
[tex]Probability=\dfrac{Favorable \ outcomes}{Total \ outcomes}[/tex]
[tex]P(\text{5 on green die })=\dfrac{1}{6}[/tex] [tex]P(\text{3 on red die })=\dfrac{1}{6}[/tex]
If any two event E and F are independent , then P(E and F)= P(E) x P(F)
P(E or F)= P(E)+P()
Find P(5 on green die and 3 on red die) = P(5 on green die) x P(3 on red die)
[tex]=\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}[/tex]
So ,P(5 on green die and 3 on red die) [tex]=\dfrac{1}{36}[/tex]
c) P(3 on green die and 5 on red die) = P(3 on green die) x P(5 on red die)
[tex]=\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}[/tex]
So ,P(3 on green die and 5 on red die) [tex]=\dfrac{1}{36}[/tex]
d) P((5 on green die and 3 on red die) or (3 on green die and 5 on red die))
= P(3 on green die and 5 on red die) + P(5 on green die and 3 on red die) (∵ Both are mutually exclusive.)
[tex]=\dfrac{1}{63}+\dfrac{1}{36}=\dfrac{2}{36}=\dfrac{1}{18}[/tex]
∴ P((5 on green die and 3 on red die) or (3 on green die and 5 on red die))
[tex]=\dfrac{1}{18}[/tex]
