131A_1_midterm_solution

131A_1_midterm_solution - EE 131A Midterm Solution Spring...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 131A Midterm Solution Spring 2008 K. Yao 1. a. S = { HHH,HHT,HTH,THH,TTH,THT,HTT,TTT } A = { HTT,HHT,HTH,HHH } B = { HHT,HTH,THH } b. A B = { HHT,HTH } . P ( A | B ) = P ( A B ) P ( B ) = 2 / 8 3 / 8 = 2 3 c. P ( B | A ) = P ( A B ) P ( A ) = 2 / 8 4 / 8 = 1 2 2. a. (Method 1) The plane fails if all 4-engines fail with a probability of q 4 or any 3 out of the 4 engines fail with a probability of C 4 3 q 3 (1 - q ) = 4 q 3 (1 - q ). Thus, p (4) = 1 - q 4 - 4 q 3 (1 - q ) = 1 - 10 - 4 - 4 × 10 - 3 × 0 . 9 = 0 . 9963 (Method 2) The plane is safe if all 4-engines are working with probability p 4 , or any 3 out of 4 engines are working with probability C 4 3 p 3 q , or any 2 out of 4 engines are working with probability C 4 2 p 2 q 2 . Thus, P (4) = p 4 + C 4 3 p 3 q + C 4 2 p 2 q 2 = (0 . 9) 4 + 4 × (0 . 9) 3 (0 . 1) + 6 × (0 . 9) 2 (0 . 1) 2 = 0 . 9963 b. (Method 1) Similarly, the plane fails if all 3 engines fail with a probability of q 3 or any 2 out of the 3 engines fail with a probability of
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

131A_1_midterm_solution - EE 131A Midterm Solution Spring...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online