A company makes three different high-end products; call them the Summit, the Cha

Question

A company makes three different high-end products; call them the Summit, the Challenger, and the Invictus. When a product is completed it is inspected for defects and then if any exist it is scrapped.

33% of production is Summits, and 10% of the Summits must be scrapped.
40% of production is Challengers, and 12% of the Challengers must be scrapped.

27% are Invictuses, and 20% of the Invictuses must be scrapped.

a. Find the probability a product must be scrapped.

b. Given a product must be scrapped, find the probability it is a Summit.

7. A company makes three different high-end products; call them the Summit, the Challenger, and the Invictus. When a product is completed it is inspected for defects and then if any exist it is scrapped. 33% of production is Summits, and 10% of the Summits must be scrapped 40% of production is Challengers, and 12% of the Challengers must be scrapped 27% are invictuses, and 20% of the Invictuses must be scrapped a. Find the probability a product must be scrapped. b. Given a product must be scrapped, find the probability it is a Summit.

Explanation / Answer

P(a product must be scraped)

=[ (0.10 × 33) + (0.12×40) +(0.2 × 27)]/100

= 13.5/100

= 0.135

b.) P( summit is scrapped | product must be scrapped)

= P( a summit is scrapped)/ P( a product must be scrapped)

=( 0.1×33/100)/0.135

= 0.033/0.135

= 0.2444

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