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Sagot :
There are 2 options to get the same number, they choose 6 from both lists or they choose 8 from both lists.
Then, the probability to select 6 from the first list is:
[tex]\frac{1}{4}[/tex]Because we have 4 options ( 2, 4, 6, 8) and 1 of then is number 6. At the same way, the probability to select 6 from the second list is:
[tex]\frac{1}{3}[/tex]Because there are 3 numbers and one of them is 6.
Finally, the probability to choose 6 from both lists is the multiplication of the probabilities above, so:
[tex]P_6=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]We can also calculate the probability to choose 8 from both lists as:
[tex]P_8=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]Because 1/4 is the probability to choose 8 from the first list and 1/3 is the probability to select 8 from the second list.
Therefore, the probability that both numbers are the same is the sum of the probability to choose 6 from both lists and the probability to choose 8 form both lists.
[tex]\begin{gathered} P=P_6+P_8 \\ P=\frac{1}{12}+\frac{1}{12} \\ P=\frac{1}{6} \end{gathered}[/tex]Answer: b. 1/6
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