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Answer:
a) 0.83 = 83% probability that a LED screen will meet specifications.
b) 0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
45% from supplier B1, 30% from supplier B2, and the rest from supplier B3.
So 100 - (45 + 30) = 100 - 75 = 25% from supplier B3.
a) Find the probability that a LED screen will meet specifications.
95% of 45%(supplier B1)
80% of 30%(supplier B2)
65% of 25%(supplier B3). So
0.83 = 83% probability that a LED screen will meet specifications.
b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.
Conditional probability.
Event A: Meets specifications.
Event B: Sent by second supplier.
0.83 = 83% probability that a LED screen will meet specifications.
This means that
Meets specifications and is sent by the second supplier.
80% of 30%, so
Probability:
0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.