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A bag contains 6 red, 4 blue, and 5 green balls. If one ball is picked at random, what is the probability that it is red or green?
2/3
11/15
4/15
1/3
11/15
Since we want red or green, add them directly (6+5=11) and divide by the total (6+4+5=15) to get the result in one step.
Red balls = 6, Blue balls = 4, Green balls = 5.
P(E)=Total┬аnumber┬аof┬аoutcomesNumber┬аof┬аfavorable┬аoutcomesтАЛ
Since we want red or green, add them directly (6+5=11) and divide by the total (6+4+5=15) to get the result in one step.
Students often include the blue balls in the numerator or mistake 'or' for multiplication instead of addition.
Calculate total outcomes
To find the total number of balls in the bag, sum the red, blue, and green balls.
6+4+5=15
Identify favorable outcomes
Since we need the probability of picking a red or green ball, sum the count of red and green balls.
6+5=11
Apply probability formula
Using the probability definition, divide the favorable outcomes by the total outcomes.
P(Red┬аor┬аGreen)=1511тАЛ
B is correct because the ratio of the sum of red and green balls to the total number of balls is 11/15.
This concept of additive probability is the foundation for solving problems involving 'at least one' scenarios in permutations and combinations.