91Ó°ÊÓ

A represents the event that the next request for assistance from a statistical software consultant relates to the SPSS package.

B represents the event that the next request is for help with SAS.

The probability for event A is \(P\left( A \right) = 0.30\).

The probability for event B is \(P\left( B \right) = 0.50\).

a.

The sum of the probabilities of both the event is not equal to 1 because, other than SPSS and SAS, other statistical software packages are also available.

b.

The probability of the provided event is computed as,

\(\begin{aligned}P\left( {A'} \right) &= 1 - P\left( A \right)\\ &= 1 - 0.30\\ &= 0.70\end{aligned}\)

Therefore, the probability of the provided event is 0.70.

c.

The probability of the provided event is computed as,

\(\begin{aligned}P\left( {A \cup B} \right) &= P\left( A \right) + P\left( B \right)\\ &= 0.30 + 0.50\\ &= 0.80\end{aligned}\)

Since A and B are disjoint events.

Therefore, the probability of the provided event is 0.80.

d.

The probability of the provided event is computed as,

\(\begin{aligned}P\left( {A' \cap B'} \right) &= P\left( {A \cup B} \right)'\\ &= 1 - P\left( {A \cup B} \right)\\ &= 1 - 0.80\\ &= 0.20\end{aligned}\)

Therefore, the probability of the provided event is 0.20.