Conditional Probability — Practice Problems and Worked Solutions

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16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Find the conditional probability.

   $$P(A\cap B)=\frac{1}{6},P(B)=\frac{1}{2}$$

   Answer: $\frac{1}{3}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{3}$$
2. 2.

   Find the conditional probability.

   $$P(A\cap B)=\frac{1}{5},P(B)=\frac{2}{5}$$

   Answer: $\frac{1}{2}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{2}$$
3. 3.

   Find the conditional probability.

   $$P(A\cap B)=\frac{3}{20},P(B)=\frac{3}{10}$$

   Answer: $\frac{1}{2}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{2}$$
4. 4.

   Find the conditional probability.

   $$P(A\cap B)=\frac{1}{4},P(B)=\frac{1}{2}$$

   Answer: $\frac{1}{2}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{2}$$
5. 5.

   Find the conditional probability.

   $$P(A\cap B)=\frac{2}{9},P(B)=\frac{2}{3}$$

   Answer: $\frac{1}{3}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{3}$$
6. 6.

   Find the conditional probability.

   $$P(A\cap B)=\frac{3}{8},P(B)=\frac{3}{4}$$

   Answer: $\frac{1}{2}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{2}$$
7. 7.

   Find the conditional probability.

   $$P(A\cap B)=\frac{1}{8},P(B)=\frac{1}{2}$$

   Answer: $\frac{1}{4}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{4}$$
8. 8.

   Find the conditional probability.

   $$P(A\cap B)=\frac{1}{10},P(B)=\frac{1}{5}$$

   Answer: $\frac{1}{2}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{2}$$
9. 9.

   Find the conditional probability.

   $$P(A\cap B)=\frac{2}{15},P(B)=\frac{2}{5}$$

   Answer: $\frac{1}{3}$

   Step-by-step solution

   1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
   2. $$=\frac{1}{3}$$
10. 10.

    Find the conditional probability.

    $$P(A\cap B)=\frac{1}{12},P(B)=\frac{1}{3}$$

    Answer: $\frac{1}{4}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{4}$$
11. 11.

    Find the conditional probability.

    $$P(A\cap B)=\frac{3}{10},P(B)=\frac{3}{5}$$

    Answer: $\frac{1}{2}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{2}$$
12. 12.

    Find the conditional probability.

    $$P(A\cap B)=\frac{1}{9},P(B)=\frac{1}{3}$$

    Answer: $\frac{1}{3}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{3}$$
13. 13.

    Find the conditional probability.

    $$P(A\cap B)=\frac{4}{15},P(B)=\frac{4}{5}$$

    Answer: $\frac{1}{3}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{3}$$
14. 14.

    Find the conditional probability.

    $$P(A\cap B)=\frac{1}{6},P(B)=\frac{1}{2}$$

    Answer: $\frac{1}{3}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{3}$$
15. 15.

    Find the conditional probability.

    $$P(A\cap B)=\frac{3}{16},P(B)=\frac{3}{8}$$

    Answer: $\frac{1}{2}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{2}$$
16. 16.

    Find the conditional probability.

    $$P(A\cap B)=\frac{2}{7},P(B)=\frac{4}{7}$$

    Answer: $\frac{1}{2}$

    Step-by-step solution

    1. $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
    2. $$=\frac{1}{2}$$

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