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### Ex4sols

Course: MATH 19731, Fall 2009
School: East Los Angeles College
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Word Count: 168

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Mathematics MATH19731 Exercise Sheet 4 Solutions 1. (a) (i) P (no major defects) = (ii) P (no defects) = 10 5 = . 12 6 4 1 = . 12 3 (b)(i) P (at least one has defects) = 1 - P (neither have defects) 4 3 10 =1- = . 12 11 11 (ii) P (neither has major defects) = 10 9 15 = . 12 11 22 2. (a) Let A = 'made by A', B = 'made by B', C = 'made by C' and D = 'defective'. Then P (D) = P (A and D) + P (B and D) + P (C and...

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Mathematics MATH19731 Exercise Sheet 4 Solutions 1. (a) (i) P (no major defects) = (ii) P (no defects) = 10 5 = . 12 6 4 1 = . 12 3 (b)(i) P (at least one has defects) = 1 - P (neither have defects) 4 3 10 =1- = . 12 11 11 (ii) P (neither has major defects) = 10 9 15 = . 12 11 22 2. (a) Let A = 'made by A', B = 'made by B', C = 'made by C' and D = 'defective'. Then P (D) = P (A and D) + P (B and D) + P (C and D) = 0.25 0.05 + 0.35 0.04 + 0.4 0.02 = 0.0345. (You can use a tree diagram here if you like.) (b) P (B|D) = P (B and D 0.35 0.04 = = 0.406. P (D) 0.0345 3 3. (a) P (2nd ball black | 1st ball black) = . 8 (b) P (4th black at 5th go) = P (BBBW B)+P (BBW BB)+P (BW BBB)+ P (W BBBB) 4 3 2 5 1 4 3 5 2 1 =( )+( ) 9 8 7 6 5 9 8 7 6 5 4 5 3 2 1 5 4 3 2 1 +( ) + ( ) 9 8 7 6 5 9 8 7 6 5 2 = = 0.032. 63 4. Let A ='A fails', B ='B fails' and C =...

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