So, |C∩F∩H|= |C U H U F| -|C| - |H| -|F| +|C∩F|+|C∩H|+|H∩F| = 450 285 195 115 +45 +70 +50 – – – = 20 Therefore 20 viewers watch all the 3 games. Only cricket viewers: |C1| = |C H - F| – = |C|-|C∩F|-|C∩H|+|C∩F∩H| = 285 -70 -45 +20 =190 only hockey viewers: |H1| = | H - C - F| = |H|-|H∩F|-|C∩H|+|C∩F∩H| = 195 -50 -70 +20 = 95 only football viewers: |F1| = | F- C - H| = |F|-|H∩F|-|C∩F|+|C∩F∩H| =115 45 -50 +20 – = 40 Therefore number of viewers who watch exactly 1 game is |C1| + |H1| + |F1| = 190 + 95 + 40 = 325. 18. Find the probability of getting a sum different from 10 or 12 rolling two dice. (5m) Jan 2015 Solution : We can get 10 in 3 different ways: 4 + 6, 5 + 5, 6 + 4, so P (10) 3/36. Similarly we get that P (12) 1/36. Since they are — — mutually exclusive events, the probability of getting 10 or 12 is P (10) + P (12) 3/36 + 1/36 — 4/36 1/9. So the probability of not getting 10 or 12 is 1 1/9 8/9. — — — — 19. Explain set operations: (6m) Jan 2015 Solution: Intersection : The common elements of two sets:
So, |C∩F∩H|= |C U H U F| -|C| - |H| -|F| +|C∩F|+|C∩H|+|H∩F| = 450 – 285 – 195 – 115 +45 +70 +50 = 20 Therefore 20 viewers watch all the 3 games. Only cricket viewers: |C1| = |C – H - F| = |C|-|C∩F|-|C∩H|+|C∩F∩H| = 285 -70 -45 +20 =190 only hockey viewers: |H1| = | H - C - F| = |H|-|H∩F|-|C∩H|+|C∩F∩H| = 195 -50 -70 +20 = 95 only football viewers: |F1| = | F- C - H| = |F|-|H∩F|-|C∩F|+|C∩F∩H| =115 – 45 -50 +20 = 40 Therefore number of viewers who watch exactly 1 game is |C1| + |H1| + |F1| = 190 + 95 + 40 = 325. 18. Find the probability of getting a sum different from 10 or 12 rolling two dice. (5m) Jan 2015 Solution : We can get 10 in 3 different ways: 4 + 6, 5 + 5, 6 + 4, so P (10) — 3/36. Similarly we get that P (12) — 1/36. Since they are mutually exclusive events, the probability of getting 10 or 12 is P (10) + P (12) — 3/36 + 1/36 — 4/36 — 1/9. So the probability of not getting 10 or 12 is 1 — 1/9 — 8/9. 19. Explain set operations: (6m) Jan 2015 Solution: Intersection : The common elements of two sets:
Unit-I-II-solutions.docx