91Ó°ÊÓ

The percentages of the accidents falling in a different type of accident-shift category are provided in a table.

The total number of accidents are 200.

a.

Let D be the event representing a day shift.

Let S be the event representing the Swing shift.

Let N be the event representing the Night shift.

Let A be the event representing the unsafe conditions.

Let B be the event representing the unrelated to conditions.

The above events can occur together as well.

The simple events are provided as,

\(S = \left\{ {\left\{ {A,D} \right\},\left\{ {A,S} \right\},\left\{ {A,N} \right\},\left\{ {B,D} \right\},\left\{ {B,S} \right\},\left\{ {B,N} \right\}} \right\}\)

b.

Using the provided table,

The probability that the selected accident was attributed to unsafe conditions is computed as,

\(\begin{aligned}P\left( A \right) &= P\left( {A \cap D} \right) + P\left( {A \cap S} \right) + P\left( {A \cap N} \right)\\ &= 0.10 + 0.08 + 0.05\\ &= 0.23\end{aligned}\)

Therefore, the probability that the selected accident was attributed to unsafe conditions is 0.23.

c.

The probability that the selected accident occur on the day shift is computed as,

\(\begin{aligned}P\left( D \right) &= P\left( {A \cap D} \right) + P\left( {B \cap D} \right)\\ &= 0.10 + 0.35\\ &= 0.45\end{aligned}\)

The probability that the selected accident did not occur on the day shift is computed as,

\(\begin{aligned}P\left( {D'} \right) &= 1 - P\left( D \right)\\ &= 1 - 0.45\\ &= 0.55\end{aligned}\)

Therefore, the probability that the selected accident did not occur on the day shift is 0.55.