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This table gives information about a group of students. Wear glasses Do not wear glasses Male 6 11 Female 9 16 (a) A student is selected at random from the group. Find, as a fraction in its lowest terms, the probability that the student is (i) a male who wears glasses, I/ (ii) a female who does not wear glasses. /1 (b) Two students are selected at random from the group. Find the probability that (i) one is a male and one is a female, (ii) at least one is a male who wears glasses. =15

This table gives information about a group of students.\newline\begin{tabular}{|c|c|c|}\newline\hline & Wear glasses & \begin{tabular}{l} \newlineDo not wear \\\newlineglasses\newline\end{tabular} \\\newline\hline Male & 66 & 1111 \\\newline\hline Female & 99 & 1616 \\\newline\hline\newline\end{tabular}\newline(a) A student is selected at random from the group.\newlineFind, as a fraction in its lowest terms, the probability that the student is\newline(i) a male who wears glasses, I/\newline(ii) a female who does not wear glasses. /11\newline(b) Two students are selected at random from the group.\newlineFind the probability that\newline(i) one is a male and one is a female,\newline(ii) at least one is a male who wears glasses. =15 =15

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Q. This table gives information about a group of students.\newline\begin{tabular}{|c|c|c|}\newline\hline & Wear glasses & \begin{tabular}{l} \newlineDo not wear \\\newlineglasses\newline\end{tabular} \\\newline\hline Male & 66 & 1111 \\\newline\hline Female & 99 & 1616 \\\newline\hline\newline\end{tabular}\newline(a) A student is selected at random from the group.\newlineFind, as a fraction in its lowest terms, the probability that the student is\newline(i) a male who wears glasses, I/\newline(ii) a female who does not wear glasses. /11\newline(b) Two students are selected at random from the group.\newlineFind the probability that\newline(i) one is a male and one is a female,\newline(ii) at least one is a male who wears glasses. =15 =15
  1. Total students: Total students = 66 (males with glasses) + 1111 (males without glasses) + 99 (females with glasses) + 1616 (females without glasses) = 4242 students.
  2. Probability of male with glasses: (i) Probability of selecting a male who wears glasses =Number of males with glassesTotal number of students=642= \frac{\text{Number of males with glasses}}{\text{Total number of students}} = \frac{6}{42}.
  3. Simplify probability fraction: Simplify 642\frac{6}{42} to its lowest terms = 17\frac{1}{7}.
  4. Probability of female without glasses: (ii) Probability of selecting a female who does not wear glasses =Number of females without glassesTotal number of students=1642= \frac{\text{Number of females without glasses}}{\text{Total number of students}} = \frac{16}{42}.
  5. Simplify probability fraction: Simplify 1642\frac{16}{42} to its lowest terms = 821\frac{8}{21}.
  6. Probability of selecting male and female: (b)(i) Probability of selecting one male and one female = (Number of malesTotal students)×(Number of femalesTotal students−1)+(Number of femalesTotal students)×(Number of malesTotal students−1)(\frac{\text{Number of males}}{\text{Total students}}) \times (\frac{\text{Number of females}}{\text{Total students} - 1}) + (\frac{\text{Number of females}}{\text{Total students}}) \times (\frac{\text{Number of males}}{\text{Total students} - 1}).

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