Question

Sally's mother has two bags of candy but she says that Sally can only have one piece from each bag. Bag #1 has 70% orange candies and 30% red candies. Bag #2 has 10% orange candies, 50% white candies, and the rest are red candies. Sally's eyes are covered and she chooses one piece of candy from each bag. What is the probability that she chooses the sam color from both bags. Make a tree diagram or area model to find the answer.

Answer 1

Bag 1 has 70% orange candies and 30% red candies so probability of orange candies when Bag is taken = 7/10 probability of red candies when Bag L is take = 3/10 Bag # 2 probability of orange candies = 1/10 probability white candies = 5/10 = 1/2 probability red candies = 4/10 = 2/5 probability that she choose same color form both bags = 7/ 10 + 1/10 + 3/10 times 2/ 5 = 7/100 + 6/50 = 7 + 12/100 = 19/100 therefore probability that she choose same color from both bags = 19/100 \r\n Area model method Bag 1 70% organ % Red 40% 0.28 0.12 50% white 0.35 0.15 10% orange 0.07 0.03 probability that she choose same color form both bag 1) 1st case both orange ball are picked probability = 0.07 2) 2nd both red balls are picked probability = 0.12 probability that she choose same color form both bags = 0.07 + 0.12 = 0.19