Given:
One letter is chosen from the word SAMPLE then a letter is chosen from the word SPACE.
a.
The sample space from the words SAMPLE and SPACE.
[tex]S=\lbrace SS,SP,SA,SC,SE,AS,AP,AA,AC,AE,MS,MP,MA,MC,ME,PS,PP,PA,PC,PE,LS,LP,LA,LC,LE,ES,EP,EA,EC,EE\rbrace[/tex]
The outcome ML is not in the sample space.
b.
The number of outcomes in the sample space n(S).
The number of letters in the word SPALE is 6.
The number of letters in the word SPACE is 5.
[tex]n(S)=6\times5=30[/tex]
The number of outcomes in the sample space is 30.
c.
Let A be the event to choose the word AA.
The number of outcome AA in the sample space is 1.
[tex]n(A)=1[/tex]
The probability of choosing the word 'AA' is P(A).
[tex]P(A)=\frac{n(A)}{n(S)}[/tex]
Substitute n(A)=1 and n(S)=30 in the equation.
[tex]P(A)=\frac{1}{30}[/tex]
The probability of choosing the word 'AA' is 1/30.
