Answer:
Explanation:
a. To find the probability of drawing either a red or a white marble in one draw, we need to add the number of red and white marbles and divide by the total number of marbles:
P(red or white) = (3 + 4) / (12 + 3 + 4) = 7/19
Therefore, the probability of drawing either a red or a white marble in one draw is 7/19.
b. To find the probability of drawing either a red, white, or blue marble in one draw, we need to add the number of red, white, and blue marbles and divide by the total number of marbles:
P(red or white or blue) = (3 + 4 + 12) / (12 + 3 + 4) = 19/19 = 1
Therefore, the probability of drawing either a red, white, or blue marble in one draw is 1.
c. To find the probability of drawing either a red marble followed by a blue marble or a red marble followed by a red marble in two draws, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two different events.
Let's calculate the probability of drawing a red marble followed by a blue marble:
P(red then blue) = (3/19) * (12/18) = 1/19
The probability of drawing a red marble on the first draw is 3/19, and the probability of drawing a blue marble on the second draw, given that a red marble was drawn on the first draw, is 12/18 (since there are now 18 marbles left, including 11 blue marbles).
Now let's calculate the probability of drawing a red marble followed by a red marble:
P(red then red) = (3/19) * (2/18) = 1/171
The probability of drawing a red marble on the first draw is 3/19, and the probability of drawing another red marble on the second draw, given that a red marble was drawn on the first draw, is 2/18 (since there are now 18 marbles left, including 2 red marbles).
Therefore, the probability of drawing either a red marble followed by a blue marble or a red marble followed by a red marble in two draws is:
P(red then blue or red then red) = 1/19 + 1/171 = 10/513
Therefore, the probability of drawing either a red marble followed by a blue marble or a red marble followed by a red marble in two draws is 10/513.