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  • Refer to Exercise 1 above. If the die were fair, determine whether or not the events A and B are independent.

Refer to Exercise 1 above. If the die were fair, determine whether or not the events A and B are independent.

Answers (1)

Given

\\A=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$ \\$\mathrm{So}, \mathrm{n}(\mathrm{A})=6, \mathrm{n}(\mathrm{S})=(6)^{2}=36$
Therefore,
\mathrm{P}(\mathrm{A})=\frac{\mathrm{n}(\mathrm{A})}{\mathrm{n}(\mathrm{S})}=\frac{6}{36}=\frac{1}{6}$
And B=\{(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)\}$
\Rightarrow \mathrm{n}(\mathrm{B})=6$
Therefore,
\\ \mathrm{P}(\mathrm{B})=\frac{\mathrm{n}(\mathrm{B})}{\mathrm{n}(\mathrm{S})}=\frac{6}{36}=\frac{1}{6}$\\ \\$A \cap B=[(5,5),(6,6)]
Therefore, \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{36}=\frac{1}{18}$

Therefore,

P (A \cap B) ≠ P(A). P(B)

Hence, A and B are not independent events.

Posted by

infoexpert22

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