A company assembles drills using components from two sources. Acemart supplies 91% of the components and Begud supplies the rest. It is known that 6% of the components supplied by Acemart are faulty and 3% of those supplied by Begud are faulty.
a) represent this info on a tree diagram (could this be explained as I don't understand how to do this with the info provided)
b) an assembled drill is selected at random- find the probability that it isn't faulty.
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a) To create a tree diagram, you can start by drawing two branches representing the two component sources: Acemart and Begud.
On the Acemart branch, write the probability of getting components from Acemart, which is 91%. Then, draw two sub-branches, one representing faulty components and the other representing non-faulty components. Write the probabilities for faulty and non-faulty components as 6% and 94%, respectively.
On the Begud branch, write the probability of getting components from Begud, which is (100% - 91% = 9%). Then, draw two sub-branches, one representing faulty components and the other representing non-faulty components. Write the probabilities for faulty and non-faulty components as 3% and 97%, respectively.
Your tree diagram should look something like this:
Acemart (91%)
/ \
Faulty (6%) Non-Faulty (94%)
Begud (9%)
/ \
Faulty (3%) Non-Faulty (97%)
b) To find the probability that an assembled drill isn't faulty, you need to consider the probabilities from both Acemart and Begud sources.
The probability of getting a non-faulty component from Acemart is 94% (0.94) and the probability of getting a non-faulty component from Begud is 97% (0.97). Since the components are sourced from both suppliers, we calculate the combined probability by multiplying these probabilities together:
Probability of a non-faulty component from Acemart * Probability of a non-faulty component from Begud
= 0.94 * 0.97
= 0.9118
Therefore, the probability that an assembled drill selected at random isn't faulty is approximately 0.9118 or 91.18%.