practice-mt-sols

practice-mt-sols - PSTAT 120A, Spring 2010, Practice...

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1. Sample space S = { all possible choices of 6 shoes from 10 pairs (i.e. 20) shoes } . | S | = ( 20 6 ) . All choices in S are equally likely. a) Let A =“no complete pairs”. P ( A ) = | A | / | S | . | A | = ± 10 6 ²± 2 1 ²± 2 1 ²± 2 1 ²± 2 1 ²± 2 1 ²± 2 1 ² = ± 10 6 ² 2 6 i.e. we ﬁrst choose 6 out of 10 pairs and then for each pair decide which shoe (left or right shoe) to be selected. Therefore P ( A ) = ( 10 6 ) 2 6 ( 20 6 ) . b) Let B =“ exactly one complete pair”. | B | = ± 10 1 ²± 2 2 ²± 9 4 ²± 2 1 ²± 2 1 ²± 2 1 ²± 2 1 ² = ± 10 1 ²± 9 4 ² 2 4 . Explanation: First pick one pair from 10 pairs and select both shoes from that pair, then pick 4 pairs from the remaining 9 pairs and pick one shoe from each of these pairs. P ( B ) = ( 10 1 )( 9 4 ) 2 4 ( 20 6 ) . c) Let C = “exactly 2 pairs”. | C | = ± 10 2 ²± 2 2 ²± 2 2 ²± 8 2 ²± 2 1 ²± 2 1 ² = ± 10 2 ²± 8 2 ² 2 2 . Explanation: First pick 2 pairs from 10 pairs and select both shoes from these pairs, then pick 2 pairs from the remaining 8 pairs and pick

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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.

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practice-mt-sols - PSTAT 120A, Spring 2010, Practice...

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