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Problem Set #4

# Problem Set #4 - e No because if one occurs the other can...

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1) Never because if one complimentary event occurs, the probability of the other occurring drops to zero, and if one does not occur, the probability of the other occurring changes to one. If the occurrence of one affects the probability of the other occurring, the events are not statistically independent. 2) a. .5 b. 1 c. 0 d. 4/6 e. ½ f. 1/6 g. 1/3 3) a. . 19281 6 =. 067 b. . . =. 58 9281 6 209 c. . =. 97281 6 34 4) a. = + =. PA B PA PB 85 b. = * = PA C PA PCA 0 c. = PAB 0 d. = + =. PB C PB PC 70 e. No because if one happens, the other cannot which means that the occurrence of one affects the probability of the other occurring, making them not independent events. 5) a. - ∩ = -. *. =. 1 PM F 1 44 58 7448 b. ∩ =. PM F 2552 6) a. ∩ = * =. PR S PR PS 135 b. =. PRS 3 c. =. PSR 45 d. ∪ = + - ∩ =. PR S PR PS PR S 615 e. No because both R and S can occur. 7) a. = =. PH G PG H 2 b. = ( ) ( ) PHG P G H P G = 23 c. = ( ) ( ) PGH P G H P H = 12 d. No because the probability of G occurring is .3, but the probability of G occurring given H has occurred is .5 and the probability of H occurring is .4 but given G has occurred, it is 2/3 e. No because if one occurs, the other can still occur.

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Unformatted text preview: e. No because if one occurs, the other can still occur. 8) a. ∩ = * =. PK J PK PJ 14 b. ∪ = + -∩ =. PK J PK PJ PK J 96 c. = ( ∩ ) ( ) PKJ P K J P K =. 2 9) a. ∩ = * =. PA B PA PB 72 b. = -∩ =. Pat least one 1 PA B 98 c. ( ∩ )+ ∩ =. P A B PA B 2 6 d. ∩ =. PA B 02 10) a. ∩ =. *. =. PS1 S2 53 53 2809 b.-∩ = -. *. =. 1 PS1 S2 1 47 47 7791 c. ∩ =. PS1 S2 2209 d. i. ∩ =. *. =. PS1 S2 58 58 3364 ii.-∩ = -. *. =. 1 PS1 S2 1 42 42 8236 iii. ∩ =. PS1 S2 1764 11) a. ∩ ∩ =. PA B C 216 b.-∩ ∩ =. 1 PA B C 784 c. ∩ ∩ =. PA B C 064 12) a. ∩ = * = * = PP1 P2 PP1 PP2P1 410 39 1290 b. ∩ + ∩ = * + * = PP1 P2 PP1 P2 410 69 610 49 4890 c. ∩ ∩ + ∩ ∩ + ∩ ∩ + ∩ ∩ = * * + * * PP1 P2 P3 PP1 P2 P3 PP1 P2 P3 PP1 P2 P3 610 59 48 610 49 58 + * * + * * = 410 69 58 610 59 48 480720 13) a. ∩ = * =. PA B PA PB 24 b.-∩ =. 1 PA B 76 c. ∩ =. PA B 24 d....
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Problem Set #4 - e No because if one occurs the other can...

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