Solution:
The probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes. That is;
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(T)} \\ \text{Where;} \\ P(A)=\text{ probability of event A} \\ n(A)=\text{ number of possible ways event A can occur} \\ n(T)=\text{ total number of possible outcomes} \end{gathered}[/tex]In a stack of 8 cards with different numbers;
The probability that the first card is an odd number and the second card is greater than 6 is the product of the probability of odd number and the probability of greater than 6. That is;
[tex]P(\text{Odd and greater than 6)}=P(odd)\times P(greater\text{ than 6)}[/tex]We have;
[tex]\begin{gathered} P(\text{odd)}=\frac{n(\text{odd)}}{n(T)} \\ P(\text{odd)}=\frac{4}{8} \\ P(\text{odd)}=\frac{1}{2} \end{gathered}[/tex]Also,
[tex]\begin{gathered} P(\text{greater than 6)=}\frac{\text{n(greater than 6)}}{n(T)} \\ P(\text{greater than 6)=}\frac{\text{2}}{8} \\ P(\text{greater than 6)=}\frac{1}{4} \end{gathered}[/tex]So, the probability that the first card is an odd number and the second is greater than 6 is;
[tex]\begin{gathered} P(\text{Odd and greater than 6)}=\frac{1}{2}\times\frac{1}{4} \\ P(\text{Odd and greater than 6)}=\frac{1}{8} \end{gathered}[/tex]FINAL ANSWER:
[tex]\frac{1}{8}[/tex]
