Question

An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found that from May through September, when it rains one day, the probability of rain for the next day is 0.3; when it does not in one day the probability of rain for the next day is 0.05 (A) Draw a waston diagram. (8) Write the transition mal (C) of it rains on Thursday, what is the probably the restaurant will be closed on Saturday on Sunday (A) Draw the transition diagram. Let A be the state in which rains (Type integers or decimals. Do not include the symbol in your answer.) (B) Write the transition matrix, P. Lot A be the state in which it rains. Α Α΄ -P (Type an integer or a decimal for each matrix clement) (C) Wit rains on Thursday, the probability of the restaurant being closed on Saturdays (Type an integer or a decimal) It rains on Thursday, the probability of the restaurant being closed on Sunday is . (Type an integer or a decimal)

Answer 1

Gren A ? stare in which it rain A': State, in which it doen't rain. Also, it rains today" then for next days P(A) 0.3 À PA'): 0.32 0.7 AA' CA Similarly, if it doesn't rain today then for next day P(A): 0.05 *P(A') 27-0.04 -0.91 AA AAA 2017 Doss A A1 & 0:3 0.05 6 Transition matone - A 0.3 A 0105 P. A AP 0.95 @ Rain on Thunday for thunday P(A) :) PIANO A 7 2 state recher To 10] A

Hence, for Inday- X,. Pxo for Sutiny * : * px, - P (PX) p² xo 00.3 0.05 0.95 0.3 0.01 10.7 0.15 20 7 2 Го: 3 0:3 0:05 0.7 0.95 TO 2 F0412074 al chances an Isaturday il 0.125 (probability for Sunday → 0.05 0.125 Xg: PY : 10.3 0.1 الم 0.89 (probabling 2 0.08125 A 0.91875 A Rain Chouces puoday 0.08210 Restaurant Closed on Kany days i probobility of it closed on satudy is 0.185 Sumery is 0.08125 boy 11 11 32