Question

Diagram 7 shows eleven cards in two boxes ,A and B.

Answer 1

Given the two boxes A and B, we can get our answers by following the steps below:

`\begin{gathered} \text{Probability = }*\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)}=(2)/(6) \\ Pr(\text{Vowels in Box B)}=(1)/(5) \\ Pr(both\text{ vowels)=Pr(Vowels in Box A)}* Pr(Vowels\text{ in Box B)} \\ Pr(\text{Both vowels)}=(2)/(6)*(1)/(5) \\ =(1)/(15) \end{gathered}`

(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:

`\begin{gathered} ((2)/(6)*(4)/(5))or((4)/(6)*(1)/(5)) \\ (8)/(30)+(4)/(30) \\ =(12)/(30) \\ =(2)/(5) \end{gathered}`

Therefore, the answer for a part is 1/15 while the answer for b part is 2/5.