Chapter 4.1, Problem 44HP

To determine

Find the correct conclusion.

Answer to Problem 44HP

  $optionD$

Explanation of Solution

Given information:

The results of the recent poll:

  $\begin{array}{lll}\hfill & For\hfill & Against\hfill \\ \mathrm{Proposition}1\hfill & 1553\hfill & 771\hfill \\ \mathrm{Proposition}2\hfill & 689\hfill & 1633\hfill \\ \mathrm{Proposition}3\hfill & 2088\hfill & 229\hfill \end{array}$

Conclusions:

  $A.$ There were $771$ votes cast against Proposition $1$ .

  $B.$ More people voted against Proposition $1$ than voted for Proposition $2$ .

  $C.$ Proposition $2$ has little chance of passing.

  $D.$ More people voted for Proposition $1$ than for Proposition $3$ .

Calculation:

Here, we have to find the conclusion that is not valid:

Now, $771$ votes as the term in the proposition $1$ row and against column.

Thus, $A$ is true.

Now, there are $771$ votes against proposition $1$ while there are only $689$ votes for proposition $2$ .

Thus, $B$ is true.

Now, proposition $2$ has $689$ votes for but $1633$ votes against. So there are more than double the votes against than votes for making the probability unlikely to pass.

Thus, $C$ is true.

Now, $1553$ people voted for proposition $1$ while $2088$ people voted for proposition $3$ . So more people voted for proposition $3$ in comparison.

Thus, $D$ is false.

Hence, $optionD$ is not valid.