A b uilding c onta ins 22 room s in to tal. 9 of the room is are on the g roun d floo r. 7 of the rooms have blue wa IIS. 4 of th e roo ms th at ar e on the grou nd floor also have blue w alls. Work out the pro babili ty tha t a ro om picked at ra ndom is ne ither on the grou nd flo or nor has blue walls. Give yo ur an swer as a fr acti on in it s simple st fo rm.

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A b uilding c onta ins 22 room s in to tal. 9 of the room is are on the g roun d floo r. 7 of the rooms have blue wa IIS. 4 of th e roo ms th at ar e on the grou nd floor also have blue w alls. Work out the pro babili ty tha t a ro om picked at ra ndom is ne ither on the grou nd flo or nor has blue walls. Give yo ur an swer as a fr acti on in it s simple st fo rm.

Answer 1

6/11

Answer 2

To calculate the probability of an event, the general method is to divide the number of ways an event can occur by the total number of possible outcomes. In this scenario, the total number of rooms is 22. The number of ground-floor rooms is 9, and among these 9, 4 also have blue walls. The total number of rooms with blue walls is 7, whether they're on the ground floor or not. From here, we can calculate the number of rooms that are either on the ground-floor or have blue walls or both. This can be given by : number of ground-floor rooms + number of rooms with blue walls - number of rooms that are both on the ground floor and have blue walls. To get the number of rooms that are neither on the ground floor, nor are painted blue, we subtract these from the total number of rooms. The requested probability is then found as the fraction: (rooms that are neither on the ground floor nor blue) / (total rooms), and simplified to its lowest terms.

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