Given the two boxes A and B, we can get our answers by following the steps below:
[tex]\begin{gathered} \text{Probability = }\times\frac{number\text{ of event outcomes}}{\text{Sample Space}} \\ Pr(\text{Vowels)=}\frac{number\text{ of vowel cards}}{\text{Total }cards} \\ Pr(\text{Vowels in Box A)}=\frac{2}{6} \\ Pr(\text{Vowels in Box B)}=\frac{1}{5} \\ Pr(both\text{ vowels)=Pr(Vowels in Box A)}\times Pr(Vowels\text{ in Box B)} \\ Pr(\text{Both vowels)}=\frac{2}{6}\times\frac{1}{5} \\ =\frac{1}{15} \end{gathered}[/tex]
(b) To get the probability that a card labelled with a vowel and a card labelled with a consonant are chosen is:
Pr(Vowels in Box A and Consonants in Box B) or Pr(Consonants in Box A and Vowels in Box B) which is given by:
[tex]\begin{gathered} (\frac{2}{6}\times\frac{4}{5})or(\frac{4}{6}\times\frac{1}{5)} \\ \frac{8}{30}+\frac{4}{30} \\ =\frac{12}{30} \\ =\frac{2}{5} \end{gathered}[/tex]
Therefore, the answer for a part is 1/15 while the answer for b part is 2/5.
