From a jar of marbles containg 4 blue marbles, 3 yellow marbles, 2 red marbles, and 1 magenta marble, you draw two marbles with replacement. Determine the following probablilites.
a. P( red then blue)
b. P(yellow and yellow)
c. P(red/yellow)
d. P(magneta/magenta)
The probability of any one color = # of that color/total. The probability of both events occurring is found by multiplying the individual probabilities.
a. 2/10 * 4/10 = ?
Use these principles to answer the remaining questions.
To solve these probabilities, we first need to determine the total number of marbles in the jar.
The total number of marbles = 4 blue marbles + 3 yellow marbles + 2 red marbles + 1 magenta marble = 10 marbles.
a. P(red then blue):
To calculate this probability, we multiply the probability of drawing a red marble on the first draw with the probability of drawing a blue marble on the second draw with replacement.
P(red then blue) = P(red) * P(blue)
The probability of drawing a red marble is 2/10 (since there are 2 red marbles out of 10 marbles).
The probability of drawing a blue marble is also 4/10 (since there are 4 blue marbles out of 10 marbles).
P(red then blue) = (2/10) * (4/10) = 8/100 = 0.08 or 8%.
b. P(yellow and yellow):
To calculate this probability, we multiply the probability of drawing a yellow marble on the first draw with the probability of drawing another yellow marble on the second draw with replacement.
P(yellow and yellow) = P(yellow) * P(yellow)
The probability of drawing a yellow marble is 3/10 (since there are 3 yellow marbles out of 10 marbles).
P(yellow and yellow) = (3/10) * (3/10) = 9/100 = 0.09 or 9%.
c. P(red/yellow):
To calculate this probability, we divide the probability of drawing a red marble given that the first marble drawn is yellow by the probability of drawing a yellow marble on the first draw.
P(red/yellow) = P(red and yellow) / P(yellow)
The probability of drawing a red and yellow marble is 2/10 * 3/10 = 6/100.
The probability of drawing a yellow marble is 3/10.
P(red/yellow) = (6/100) / (3/10) = 6/30 = 1/5 = 0.2 or 20%.
d. P(magenta/magenta):
Since there is only 1 magenta marble, the probability of drawing a magenta marble is 1/10.
P(magenta/magenta) = (1/10) * (1/10) = 1/100 = 0.01 or 1%.