I am working through probability questions in a maths book.
The Sample Space is defined as the "list of all possible outcomes".
The probability of an event is defined as P(E) = Number of favourable outcomes/Number of Possible outcomes.
I am OK with the formula above.
There is a question with a circular spinner, divided into four quadrants: two are coloured red and two are coloured blue. It says to state the Sample Space. I put down {Red, Red, Blue, Blue} the answer at the back of the book is {Red, Blue}. It then asks to calcuate the probability of the spinner landing on red. I calculated P(Red) = Number of favourable outcomes/Number of possible outcomes = 2/4 = 1/2 same answer but different sample spaces.
Another question is a spinner divided into five segments, 1 green, 2 yellow and 2 red. Again to list the sample space I put down {Green, Yellow, Yellow, Red, Red} they list {Green, Yellow, Red}. To find the probability of the spinner landing on green I put: P(Green) = Number of favourable outcomes/Number of possible outcomes = 1/5. The book has the same answer but I can't see how they worked it from the probability space with only 3 outcomes.
I have been on lots of websites, some list sample spaces similar to mine - each colour is listed as many times as it appears and the calculation follows the formula. Most however, seem to follow the book - each colour is listed once. They get the same answers but don't use the formula, they just seem to count each colour as a different outcome when they do the calculation.
Am I missing a trick or is it just up to the person how they wish to do the sample space.
Any insight would be appreciated
The Sample Space is defined as the "list of all possible outcomes".
The probability of an event is defined as P(E) = Number of favourable outcomes/Number of Possible outcomes.
I am OK with the formula above.
There is a question with a circular spinner, divided into four quadrants: two are coloured red and two are coloured blue. It says to state the Sample Space. I put down {Red, Red, Blue, Blue} the answer at the back of the book is {Red, Blue}. It then asks to calcuate the probability of the spinner landing on red. I calculated P(Red) = Number of favourable outcomes/Number of possible outcomes = 2/4 = 1/2 same answer but different sample spaces.
Another question is a spinner divided into five segments, 1 green, 2 yellow and 2 red. Again to list the sample space I put down {Green, Yellow, Yellow, Red, Red} they list {Green, Yellow, Red}. To find the probability of the spinner landing on green I put: P(Green) = Number of favourable outcomes/Number of possible outcomes = 1/5. The book has the same answer but I can't see how they worked it from the probability space with only 3 outcomes.
I have been on lots of websites, some list sample spaces similar to mine - each colour is listed as many times as it appears and the calculation follows the formula. Most however, seem to follow the book - each colour is listed once. They get the same answers but don't use the formula, they just seem to count each colour as a different outcome when they do the calculation.
Am I missing a trick or is it just up to the person how they wish to do the sample space.
Any insight would be appreciated