Let's find the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die.
Where:
• Number of diamonds in a deck of cards = 13
,• Number of spade cards in a deck of cards = 13
,• Total number of cards in a standard deck = 52
,• Number of 2 on a six-sided die = 1
To find the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die, apply the formula:
P(diamond or spade and rolling a 2) = P(diamond or spade) or P(2)
Thus, we have:
[tex]\begin{gathered} P(\text{diamond or spade)=}P(\text{diamond) + P(spade) = }\frac{13}{52}+\frac{13}{52}=\frac{26}{52}=\frac{1}{2} \\ \\ P(\text{rolling a 2) = }\frac{1}{6} \end{gathered}[/tex]Therefore, we have:
[tex]P(\text{diamond or spade) and P(2) = P}(\text{diamond or spade)}\ast P(2)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}=0.083[/tex]Therefore, the probability is: = 0.083
Let's convert to percent by mutiplying thr probability by 100:
[tex]0.083\times100=8.3\text{ \%}[/tex]ANSWER:
8.3%
