Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-003 · ★☆☆ Basic
Three machines make 50 %, 30 % and 20 % of the parts, with 1 %, 2 % and 5 % defective respectively. What fraction of all parts is defective?
Choose one option.
Show answer
- A. 0.021
Explanation
\(0.5\cdot0.01+0.3\cdot0.02+0.2\cdot0.05=0.005+0.006+0.010=0.021\).
Review the concept: Law of total probability
The total probability of an event \(A\) is the weighted average of its conditional probabilities \(P(A\mid B_i)\) over a partition \(B_i\) of the sample space, with the probability of each case as its weight.
\[P(A)=\sum_{i=1}^{n}P(A\mid B_i)\,P(B_i)\]
More practice problems: law of total probability
- ZW-LAW-OF-TOTAL-PROBABILITY-001 Events B_1,B_2 form a partition with P(B_1)=0.4, P(B_2)=0.6, P(A| B_1)=0.5 and P(A| B_2)=0.2. What…
- ZW-LAW-OF-TOTAL-PROBABILITY-002 Urn A has 3 red and 2 blue balls; urn B has 1 red and 4 blue. A fair coin picks an urn and a ball i…
- ZW-LAW-OF-TOTAL-PROBABILITY-004 What must a family B_1,dots,B_n satisfy to be used in the law of total probability?
- ZW-LAW-OF-TOTAL-PROBABILITY-005 It rains with probability 0.3. If it rains you are late with probability 0.5; otherwise 0.1. What i…
- ZW-LAW-OF-TOTAL-PROBABILITY-006 Two cards are drawn without replacement from a 52-card deck. What is the probability that the secon…
- ZW-LAW-OF-TOTAL-PROBABILITY-007 Given P(A)=0.5, P(B)=0.5 and P(A| B)=0.8, what is P(A| B^c)?
- ZW-LAW-OF-TOTAL-PROBABILITY-008 A die is rolled. On a 6 a ball is drawn from an urn where P(red) is 1/2; otherwise from another whe…
- ZW-LAW-OF-TOTAL-PROBABILITY-009 If 0<P(B)<1 and P(A| B)=P(A| B^c)=p, what is P(A)?
← ZW-LAW-OF-TOTAL-PROBABILITY-002 ZW-LAW-OF-TOTAL-PROBABILITY-004 →