Final answer:
To calculate the probability of drawing a blue crayon and then a green crayon without replacement from a bag, you multiply the probability of drawing a blue crayon first (4/7) by the probability of drawing a green crayon second (1/6), getting a result of 1/10.5, or approximately 0.095.
Step-by-step explanation:
The subject is about calculating the probability of selecting crayons in a specific order from a bag without replacement. To find the probability of selecting a blue crayon first and then a green crayon, we perform two steps:
Calculate the probability of drawing a blue crayon first:
There are 2 red crayons, 4 blue crayons, and 1 green crayon in the bag. The total number of crayons is 7. The probability of drawing a blue crayon first is the number of blue crayons divided by the total number of crayons, which is 4/7.
Calculate the probability of drawing a green crayon after a blue one has been drawn:
After a blue crayon is drawn, there is 1 less crayon in the bag, so the total number of crayons is now 6. Since the blue crayon is kept out, there are still 2 red crayons and 1 green crayon.
The probability of drawing the green crayon now is 1/6.
To find the combined probability of both events occurring in sequence (blue, then green), we multiply the individual probabilities:
P(blue, then green) = P(blue) × P(green after blue)
= (4/7) × (1/6)
= 4/42
= 1/10.5.
Therefore, the probability of drawing a blue crayon and then a green one is 1/10.5, or approximately 0.095.