Answer :
Final answer:
To find the probability of drawing at least two blue marbles from a bag of 6 red and 4 blue marbles in four tries without replacement, calculate the probability for each possible scenario (drawing two, three, or four blue marbles) and add them together.
Explanation:
The subject of this question is probability, specifically probability without replacement. In Susie's bag, there are 10 marbles in total - 6 red and 4 blue. She is selecting four marbles without replacement, meaning she doesn't put the marbles back into the bag after drawing one.
We're looking to find the probability that at least two of the marbles drawn will be blue. This could mean two, three, or even all four marbles are blue. Therefore, we need to find the probability for each of these scenarios and then add them together.
The probability of drawing two blue marbles and two red marbles is calculated as (4/10*3/9*6/8*5/7) * 6, where the factor of 6 accounts for the different sequences of drawing two blues and two reds.
The probability of drawing three blue marbles and one red marble is calculated as (4/10*3/9*2/8*6/7) * 4, accounting for the four possible sequences of drawing three blues and one red.
Finally, the probability of drawing four blue marbles is simply 4/10*3/9*2/8*1/7.
By adding these probabilities together, we get the total probability of drawing at least two blue marbles in four draws without replacement.
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