DEFINITIONS

Definition conditional probability:

\(P(B|A)=\frac{P(A \cap B)}{P(A)}=\frac{P(A\ and\ B)}{P(A)}\)

SOLUTION

\(\begin{array} {lc} & \text{Gender} \ \text {Longer finger} & \begin{array}{l|c|r|r} & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Index finger } & 78 & 45 & 123 \\\hline \text{ Ring finger } & 82 & 152 & 234 \\ \hline \text { Same length } & 52 & 43 & 95 \\ \hline \text { Total } & 212 & 240 & 452 \end{array}\ \end{array}\)

R=ring finger longer

F=female

We note that the table contains information about 452 students (given in the bottom right corner of the table).

Moreover, 123+95=218 of the 452 students are female, because 123 and 95 are mentioned in the row "Index Finger/Same Length" and in the column "Total" of the table.

The probability is the number of favorable outcomes divided by the number of possible outcomes:

\(P(R^c)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{218}{452}\)

Next, we note that 45+43=88 of the 452 students are males that don't have a longer ring finger, because 45 and 43 are mentioned in the row "Index finger/Same Length" and in the column "Male" of the given table.

\(P(R^c\ and\ F^c)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{88}{452}\)

Use the definition of conditional probability:

\(P(F^c|R^c)=\frac{P(R^c\ and\ F^c)}{P(R^c)}=\frac{88/452}{218/452}=\frac{88}{218}=\frac{44}{109}\approx0.4037=40.37\%\)

40.37% of the people with no longer right finger are males.

Result:

\(\frac{44}{109}\approx0.4037=40.37\%\)

40.37% of the people with no longer right finger are males.

Definition conditional probability:

\(P(B|A)=\frac{P(A \cap B)}{P(A)}=\frac{P(A\ and\ B)}{P(A)}\)

SOLUTION

\(\begin{array} {lc} & \text{Gender} \ \text {Longer finger} & \begin{array}{l|c|r|r} & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Index finger } & 78 & 45 & 123 \\\hline \text{ Ring finger } & 82 & 152 & 234 \\ \hline \text { Same length } & 52 & 43 & 95 \\ \hline \text { Total } & 212 & 240 & 452 \end{array}\ \end{array}\)

R=ring finger longer

F=female

We note that the table contains information about 452 students (given in the bottom right corner of the table).

Moreover, 123+95=218 of the 452 students are female, because 123 and 95 are mentioned in the row "Index Finger/Same Length" and in the column "Total" of the table.

The probability is the number of favorable outcomes divided by the number of possible outcomes:

\(P(R^c)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{218}{452}\)

Next, we note that 45+43=88 of the 452 students are males that don't have a longer ring finger, because 45 and 43 are mentioned in the row "Index finger/Same Length" and in the column "Male" of the given table.

\(P(R^c\ and\ F^c)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{88}{452}\)

Use the definition of conditional probability:

\(P(F^c|R^c)=\frac{P(R^c\ and\ F^c)}{P(R^c)}=\frac{88/452}{218/452}=\frac{88}{218}=\frac{44}{109}\approx0.4037=40.37\%\)

40.37% of the people with no longer right finger are males.

Result:

\(\frac{44}{109}\approx0.4037=40.37\%\)

40.37% of the people with no longer right finger are males.