Generating...                               quiz01_n18

  1. From a group of 6 men and 8 women, how many different committees consisting of 4 men and 3 women can be formed?

    $\binom{ 6}{ 1} \times \binom{ 8}{ 1} = 48$ $\binom{ 6}{ 4} \times \binom{ 8}{ 3} = 840$ $\binom{ 6}{ 4} + \binom{ 8}{ 3} = 71$ $\binom{ 14}{ 7} = 3432$

  2. Two six-sided dice are thrown sequentially, and the face values that come up are recorded. Let $A$ be the event that the sum of two values is 4. Then find $P(A^c)$.

    $\displaystyle {{8}\over{9}}$ $\displaystyle {{9}\over{10}}$ $\displaystyle {{17}\over{18}}$ $\displaystyle {{11}\over{12}}$

  3. Suppose that $P(A) = {{3}\over{5}}$, $P(B) = {{1}\over{2}}$, and $P(A\cap B) = {{1}\over{5}}$. Find $P(A^c\cap B^c)$.

    $\displaystyle {{4}\over{5}}$ $\displaystyle {{9}\over{10}}$ $\displaystyle {{1}\over{10}}$ $\displaystyle {{3}\over{10}}$

  4. Two six-sided dice are thrown sequentially, and the face values that come up are recorded. Let $A$ be the event that the sum of two values is 9, and $B$ be the event that the sum of two values is 6. Then find $P(A\cup B)$.

    $\displaystyle {{5}\over{36}}$ $\displaystyle {{1}\over{9}}$ $\displaystyle {{2}\over{9}}$ $\displaystyle {{1}\over{4}}$ $\displaystyle {{5}\over{18}}$

  5. A committee of 3 must be formed from a group of 11. How many different committees are possible?

    $\binom{ 14}{ 11} = 364$ $\binom{ 11}{ 1} = 11$ $\binom{ 11}{ 3} = 165$ $\binom{ 14}{ 3} = 364$

  6. Suppose that $P(A) = {{1}\over{2}}$, $P(B) = {{3}\over{5}}$, and $P(A\cap B) = {{2}\over{5}}$. Find $P(A\cup B)$.

    $\displaystyle {{7}\over{10}}$ $\displaystyle -{{1}\over{10}}$ $\displaystyle {{3}\over{10}}$ $\displaystyle {{11}\over{10}}$

  7. A coin is tossed repeatedly until heads are observed 4 times. How many different outcomes (or patterns) are possible if the 4-th heads is observed at 6-th attempt of coin-tossing.

    $\binom{ 5}{ 4} = 5$ $\binom{ 6}{ 4} = 15$ $\binom{ 6}{ 3} = 20$ $\binom{ 5}{ 3} = 10$

  8. There are 5 red blocks and 5 blue blocks. How many patterns can you make by placing them in a line?

    $\binom{ 10}{ 1} = 10$ $\binom{ 5}{ 5} = 1$ $\binom{ 10}{ 5} = 252$ $\binom{ 25}{ 1} = 25$

  9. Find the coefficient of $\displaystyle x^5\,y^3$ in the expansion of $\displaystyle \left(y+x\right)^8$ .

    $\binom{ 8}{ 5} = 56$ $\binom{ 8}{ 1} = 8$ $\binom{ 5}{ 3} = 10$ $\binom{ 15}{ 1} = 15$

  10. Suppose that $P(A) = {{3}\over{5}}$, $P(B) = {{7}\over{10}}$, and $P(A\cap B) = {{2}\over{5}}$. Find $P(A\cap B^c)$.

    $\displaystyle {{3}\over{10}}$ $\displaystyle {{4}\over{5}}$ $\displaystyle {{1}\over{5}}$ $\displaystyle {{2}\over{5}}$


Department of Mathematics
Last modified: 2025-06-19