Question 1

Use the table below to find the probability of selecting a person at random, that the personYes (Y)No (N)Don't Know (D)TotalMen (M)15212373348Women (W)14910994352Total301232167700is male and responded no. is a woman and responded don't know. responded yes given that the person was a male.responded don't know given that the person was a woman.

Use the table below to find the probability of selecting a person at random, that-example-1

Question 2

Recall that:

$P(success)=\frac{favorable\text{ outcomes}}{total\text{ outccomes}}.$

Therefore:

$\begin{gathered} P(male\text{ and no\rparen=}(123)/(700), \\ P(woman\text{ and don't know\rparen=}(94)/(700). \end{gathered}$

Now, recall that:

$P(A|B)=(P(A\cap B))/(P(B)).$

Therefore:

$\begin{gathered} P(yes|male)=\frac{P(male\text{ and yes\rparen}}{P(male)}=((152)/(700))/((348)/(700))=(152)/(348), \\ P(don^(\prime)t\text{ know\mid woman\rparen=}((94)/(700))/((352)/(700))=(94)/(352). \end{gathered}$

Simplifying all of the above results, we get:

$\begin{gathered} P(male\text{ and no\rparen=}(123)/(700), \\ P(woman\text{ and don't know\rparen=}(47)/(350), \\ P(yes|male)=(38)/(87), \\ P(don^(\prime)t\text{ know\mid woman\rparen=}(47)/(176). \end{gathered}$

Answer:

$\begin{gathered} P(male\text{ and no}\operatorname{\rparen}\text{=}(123)/(700)\text{, } \\ P(woman\text{ and don't know\rparen=}(47)/(350), \\ P(yes|male)=(38)/(87), \\ P(don^(\prime)t\text{ know\mid woman\rparen=}(47)/(176). \end{gathered}$

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