Exam 12: From Randomness to Probability

Correct Answer:

Verified

a.
$$\begin{array} { l } P ( \text { neither ham nor turkey } ) \\= 1 - P ( \text { ham } \cup \text { turkey } ) \\= 1 - [ P ( \text { ham } ) + P ( \text { turkey } ) - P ( \text { ham } \cap \text { turkey } ) ] \\= 1 - [ 0.44 + 0.58 - 0.16 ] = 1 - 0.86 = 0.14\end{array}$$
Or, using the Venn diagram at the right, $14 \%$
b.
$$\begin{aligned}P ( \text { ham only } ) & = P ( \text { ham } ) - P ( \text { ham } \cap \text { turkey } ) \\& = 0.44 - 0.16 \\& = 0.28\end{aligned}$$
Or, using Venn Diagram at the right, $28 \%$ .

c. $\quad P ($ ham $\mid$ turkey $) = \frac { P ( \text { ham } \cap \text { turkey } ) } { P ( \text { turkey } ) } = \frac { 0.16 } { 0.58 } = 0.2759$ d.No, the events are not disjoint, since some families (16%) have both ham and turkey at
their holiday meals.

Correct Answer:

Verified

Overall, 102 of 136, or 75%, preferred Spanish.35 of 51, or 68.6%, of students in Chemistry
had Spanish.23 of 33, or 69.6%, of students in Physics had Spanish, and 44 of 52, or 84.6%
of students in Biology had Spanish.Chemistry and Physics students were somewhat less
likely to take Spanish than Biology students.It appears that there is an association between
preference in science and foreign language.