during the repair of a large number of car engines, the spark-plugs were changed in 70% and the air-filter in 45% of case, and that both parts were changed 31.5% of case so
- is the replacement of spark-plugs independent of the replacement of the air filter? and reason ?
-find the probability that in repairing an engine for which the spark-plugs have been changed it with also be necessary to replacement the air-filter?

Question

during the repair of a large number of car engines, the spark-plugs were changed in 70% and the air-filter in 45% of case, and that both parts were changed 31.5% of case so
- is the replacement of spark-plugs independent of the replacement of the air filter? and reason ?
-find the probability that in repairing an engine for which the spark-plugs have been changed it with also be necessary to replacement the air-filter?

kropot72 · Answer

Let the replacement of spark-plug be event A and the replacement of the air-filter vbe event B. Events A and B are independent if (and only if) the following is true:
$$P(A \cap B)=P(A) \times P(B)$$
In this case 
$$P(A \cap B)=0.315$$
P(A) = 0.7 and P(B) = 0.45
Can you now find whether or not the events are independent?

kropot72 · Answer

air-filter be event B*

kropot72 · Answer

$$P(A) \times P(B)=0.7\times 0.45=you\ can\ calculate$$

kropot72 · Answer

@mannuvirk90 Are you there?