Answer to Question #199334 in Statistics and Probability for Bahawal tahir

Question

A pilot plant has produced metallurgical batches which are summarized as follows: Low strength High... 1 answer below »

A pilot plant has produced metallurgical batches which are summarized as follows:

Low strength

High strength

Low in impurities

2

27

High in impurities

12

4

If these results are representative of full-scale production, find estimated probabilities that a production batch will be:

i) low in impurities

ii) high strength

iii) both high in impurities and high strength

iv) both high in impurities and low strength​

Answer 1

Total number of results = 2+ 27+12+4 =45

(i) P(low in impurities ) = $\dfrac{2+27}{45}=\dfrac{29}{45}=0.645$

(ii) P(high strength ) = $\dfrac{27+4}{45}=\dfrac{31}{45}=0.689$

(iii) P(both high in impurities and high strength ) = $\dfrac{4}{45}=0.0889$

(iv) P(both high in impurities and low strength) = $\dfrac{12}{45}=0.2667$