Jorgen has 20 sweets in his pocket. The sweets are either blue or yellow. He picks a sweet and eats it and takes another sweet and eats it again. The probability of him picking two blue sweets is 6/30. How many yellow sweets does he have in his pocket.
1st step: Firstly we know 3 things: 1. There are 20 sweets in total 2. The sweets are either blue or yellow 3. The probability of picking two blue sweets in 6/30 We let the total number of blue sweets in his pocket be 'n'. Then: The probability of him picking a blue sweet is n/20 He now has one less blue sweets, so we can represent this as (n-1). As he has one less sweet, the total amount of sweets in his pocket are 19. Therefore (n-1) / 19 2nd step: As we want the probability of getting a blue sweet AND then another blue sweet, the AND signals multiplication. Therefore we multiply the two probabilities together. We then equate this to 6/30 as the probabilitiy of 2 blue sweets is 6/30. n/20 x (n-1) / 19 = 6/30 This simplifies to n2 - n - 76 = 0 3rd Step: We need to solve this quadratic equation using quadratic fomula. we get 2 values; 9.2 and a negative value. we ignore the negative as we cant have a negative number of sweets. Also we cant have 9.2 sweets so we round this down to 9. 4th Step: As we know Jorgen has 9 sweets. Take 9 from 20 to get 11.
