Probability Rules — Practice Problems and Worked Solutions

The formulas you need here

17 worked problems

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

1. 1.

   Find the probability of A or B.

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

   Answer: $\frac{2}{3}$

   Step-by-step solution

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

   Find the probability of A or B.

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

   Answer: $\frac{7}{10}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{7}{10}$$
3. 3.

   Find the probability of A or B.

   $$P(A)=\frac{3}{10},P(B)=\frac{2}{5},P(A\cap B)=\frac{1}{10}$$

   Answer: $\frac{3}{5}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{3}{5}$$
4. 4.

   Find the probability of A or B.

   $$P(A)=\frac{3}{4},P(B)=\frac{1}{2},P(A\cap B)=\frac{2}{5}$$

   Answer: $\frac{17}{20}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{17}{20}$$
5. 5.

   Find the probability of A or B.

   $$P(A)=\frac{2}{3},P(B)=\frac{1}{4},P(A\cap B)=\frac{1}{6}$$

   Answer: $\frac{3}{4}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{3}{4}$$
6. 6.

   Find the probability of A or B.

   $$P(A)=\frac{4}{5},P(B)=\frac{3}{10},P(A\cap B)=\frac{1}{5}$$

   Answer: $\frac{9}{10}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{9}{10}$$
7. 7.

   Find the probability of A or B.

   $$P(A)=\frac{1}{3},P(B)=\frac{1}{2},P(A\cap B)=\frac{1}{12}$$

   Answer: $\frac{3}{4}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{3}{4}$$
8. 8.

   Find the probability of A or B.

   $$P(A)=\frac{3}{5},P(B)=\frac{1}{5},P(A\cap B)=\frac{1}{10}$$

   Answer: $\frac{7}{10}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{7}{10}$$
9. 9.

   Find the probability of A or B.

   $$P(A)=\frac{1}{2},P(B)=\frac{2}{5},P(A\cap B)=\frac{3}{20}$$

   Answer: $\frac{3}{4}$

   Step-by-step solution

   1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
   2. $$=\frac{3}{4}$$
10. 10.

    Find the probability of A or B.

    $$P(A)=\frac{5}{8},P(B)=\frac{1}{4},P(A\cap B)=\frac{1}{8}$$

    Answer: $\frac{3}{4}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{3}{4}$$
11. 11.

    Find the probability of A or B.

    $$P(A)=\frac{2}{7},P(B)=\frac{3}{7},P(A\cap B)=\frac{1}{7}$$

    Answer: $\frac{4}{7}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{4}{7}$$
12. 12.

    Find the probability of A or B.

    $$P(A)=\frac{7}{10},P(B)=\frac{2}{5},P(A\cap B)=\frac{3}{10}$$

    Answer: $\frac{4}{5}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{4}{5}$$
13. 13.

    Find the probability of A or B.

    $$P(A)=\frac{1}{4},P(B)=\frac{1}{3},P(A\cap B)=\frac{1}{12}$$

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

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{1}{2}$$
14. 14.

    Find the probability of A or B.

    $$P(A)=\frac{5}{6},P(B)=\frac{1}{3},P(A\cap B)=\frac{1}{4}$$

    Answer: $\frac{11}{12}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{11}{12}$$
15. 15.

    Find the probability of A or B.

    $$P(A)=\frac{3}{8},P(B)=\frac{1}{2},P(A\cap B)=\frac{3}{16}$$

    Answer: $\frac{11}{16}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{11}{16}$$
16. 16.

    Find the probability of A or B.

    $$P(A)=\frac{9}{10},P(B)=\frac{1}{5},P(A\cap B)=\frac{1}{10}$$

    Answer: $1$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=1$$
17. 17.

    Find the probability of A or B.

    $$P(A)=\frac{2}{5},P(B)=\frac{3}{10},P(A\cap B)=\frac{1}{10}$$

    Answer: $\frac{3}{5}$

    Step-by-step solution

    1. $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
    2. $$=\frac{3}{5}$$

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• Expected Value
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• Normal Distribution
• Confidence Intervals
• Hypothesis Tests
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