Final answer:
The probability of selecting two red balls without replacement from a box that contains 3 red, 2 green, and 1 blue ball is calculated by multiplying the probability of selecting the first red ball (1/2) by the probability of selecting the second red ball given the first has already been selected (2/5), resulting in a final probability of 1/5 or 0.2.
Step-by-step explanation:
The question asks about the probability of selecting two red balls from a box that contains 3 red balls, 2 green balls, and 1 blue ball, without replacement. To find this probability, we can use the formula P(A and B) = P(A) × P(B after A).
First, the probability of drawing one red ball, P(A), is the number of red balls divided by the total number of balls: 3/6 or 1/2. Next, if one red ball has already been drawn, there are now 2 red balls left and only 5 balls in total. So the probability of drawing a second red ball, P(B after A), is 2/5.
Thus, the probability of drawing two red balls without replacement is (1/2) × (2/5) = 1/5 or 0.2.