A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat
ham, and 16% have both turkey and ham to eat at holiday meals.
a.What is the probability that a family selected at random had neither turkey nor ham at
their holiday meal?
b.What is the probability that a family selected at random had only ham without having
turkey at their holiday meal?
c.What is the probability that a randomly selected family having turkey had ham at their
holiday meal?
d.Are having turkey and having ham disjoint events? Explain.

Question

Quizplus · Accepted Answer

The Answer is a.

\begin{array} { l } P ( ext { neither ham nor turkey } ) \= 1 - P ( ext { ham } \cup ext { turkey } ) \= 1 - [ P ( ext { ham } ) + P ( ext { turkey } ) - P ( ext { ham } \cap ext { turkey } ) ] \= 1 - [ 0.44 + 0.58 - 0.16 ] = 1 - 0.86 = 0.14\end{array}

Or, using the Venn diagram at the right,

14 \%

b.

\begin{aligned}P ( ext { ham only } ) & = P ( ext { ham } ) - P ( ext { ham } \cap ext { turkey } ) \& = 0.44 - 0.16 \& = 0.28\end{aligned}

Or, using Venn Diagram at the right,

28 \%

.

c.

\quad P (

ham

\mid

turkey

) = \frac { P ( ext { ham } \cap ext { turkey } ) } { P ( ext { turkey } ) } = \frac { 0.16 } { 0.58 } = 0.2759

$a. \begin{array} { l } P ( ext { neither ham nor turkey } ) \ = 1 - P ( ext { ham } \cup ext { turkey } ) \ = 1 - [ P ( ext { ham } ) + P ( ext { turkey } ) - P ( ext { ham } \cap ext { turkey } ) ] \ = 1 - [ 0.44 + 0.58 - 0.16 ] = 1 - 0.86 = 0.14 \end{array} Or, using the Venn diagram at the right, 14 \% b. \begin{aligned} P ( ext { ham only } ) & = P ( ext { ham } ) - P ( ext { ham } \cap ext { turkey } ) \ & = 0.44 - 0.16 \ & = 0.28 \end{aligned} Or, using Venn Diagram at the right, 28 \% . c. \quad P ( ham \mid turkey ) = \frac { P ( ext { ham } \cap ext { turkey } ) } { P ( ext { turkey } ) } = \frac { 0.16 } { 0.58 } = 0.2759 d.No, the events are not disjoint, since some families (16%) have both ham and turkey at their holiday meals.$ d.No, the events are not disjoint, since some families (16%) have both ham and turkey at
their holiday meals.

A Survey of Families Revealed That 58% of All Families