Spin the Pointer (21 points) To Show their appreciation, Delectable Delights decided to put on a carnival for its employees. One of the games at the carnival was Spin the Pointer, which uses a spinner like the one pictured here. A carnival ticket is required to play the game. The spinner is divided into 8 equally sized sectors. Thus, the spinner has an equal probabity of landing in each sector. Sector Sector I Sector 1 I Sector 2 I Sector 3 I Sector 4 I Sector 5 I Sector 6 I Sector 7 Sector (a) What is the sample space for the spinner game? Use appropriate symbol. (3 points) TAT 3090 LAB 5: PROBABILITY FALL 2022 S= {1, 2, 3, 4, 5, 6, 7, 8} (b) What is the probability of landing in each sector? Use probability notation. (3 points) P (sector l)= 1/8 P (sector 2)= 1/8 P (sector 3)= 1/8 P (sector 4)= 1/8 P (sector 5)= 1/8 P (sector 6)= 1/8 P (sector 7)= 1/8 P (sector 8)= 1/8 (c) The number shows on each sector is the money a player receives after playing one spin of the game. That is, if the spinner lands in Sector 1 or Sector 5, the player receives $1.00; if the spinner lands in Sector 3, the player receives $5.00; if the spinner lands in the rest sectors, the player receives nothing. Sector Sector Sector 1 Sector 2 Sector 1 Sector 3 Sector 8 $1.00 Sector 4 $0.00 Sector 5 Sector 6 Sector 7 $0.00 Sector 2 Sector 7 $0.00 Sector 8 Sector 3 Sector 6 $5.00 $0.00 Sector 5 $1.00 Sector 4 $0.00 Sector i. Let event A be the player receives $1.00 after one spin of the game. What is the probability of event A occurring? Use probability notation. (3 points) P(A)= 1/4 =probability of event A occurringii. Let event C be the player receives $5.00 after one spin of the game. What is the probability of event C occurring? Use probability notation. (3 points) STAT 3090 LAB 5: PROBABILITY FALL 2022 probability of event C occurring = number of sectors receiving $5ITotal number of sectors P(C)= 1/8 =probability of event C occurring iii. Let event D be the player receives $000 after one spin of the game. What is the probability of event D occurring? Use probability notation. (3 points) probability of event D occurring =number of sectors receiving $0/Total number of sectors P(D)= 5f8= 62.5% =probability of event D occurring iv. Describe the complement of event D. Calculate the probability of event D occurring by the complement rule. Use probability notation. (3 points) D= $0.00 after 1 spin D= not $0.00 after 1 spin P(Not Event D) = 1P(Event D) P(DC)=1-P(D)= 1 5/8 = 3f8 P(D)= 3/8 =probability of event D occurring by the complement rule (d) Suppose a player needs to pay for the carnival ticket costs $1.00 before playing every spin of the game. What is the probability the player has a prot of $4.00 after one spin of the game? Explain how you obtained your answer. (3 points) P (sector 3)= 1.18 Since the player needs to pay $1 before every spin, the only way to have a prot of $4 after the lSt spin is to land on a sector with $5 there is only 1 sector with $5-sector 3- so, the probability of $4 prot is the same as the probability of landing on sector 3