The question tells us there is a rolling die with 6 faces.
This means that the probability of getting any number after rolling the die is equal for all values of die.
i.e.
[tex]\begin{gathered} P(\text{any value on die)=}\frac{1}{6} \\ \\ i\mathrm{}e\text{.} \\ P(1)=\frac{1}{6} \\ P(2)=\frac{1}{6} \\ P(3)=\frac{1}{6} \\ \\ \ldots\text{and so on} \end{gathered}[/tex]The number of cards in the deck is: 5 red + 7 blue + 8 yellow = 20 cards altogether.
Thus, if we pick a blue card from this deck of 20 cards, the probability is:
[tex]\begin{gathered} P(\text{blue)}=\frac{n\text{umber of blue cards}}{\text{total number of cards}} \\ \\ P(\text{blue)}=\frac{7}{20} \end{gathered}[/tex]Therefore, if these two events - rolling a die and picking a blue card - occur at the same time, then we use the AND probability to solve.
This is done below:
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