If you draw one marble from a jar containing 7 red, 5 blue, 8 green marbles, with replacement, what is the probability the marble drawn is blue?

If you draw one marble from a jar containing 7 red, 5 blue, 8 green marbles, with replacement, what is the probability the marble drawn is blue?

• A. 3/20
• B. 1/4
• C. 1/5
• D. 7/20

Answer: (B)

The chance of drawing blue in a single draw with replacement is the blue portion of the jar: blue count over total count. There are five blue marbles out of twenty total marbles, so the probability is 5/20, which simplifies to 1/4. With replacement, the jar’s composition stays the same for every draw, so this probability remains constant. Therefore, the correct probability is one quarter. The other fractions would imply a different number of blue marbles than are actually in the jar (for example, 3/20 would require only three blue marbles, and 1/5 would correspond to four blue marbles, etc.).

The chance of drawing blue in a single draw with replacement is the blue portion of the jar: blue count over total count. There are five blue marbles out of twenty total marbles, so the probability is 5/20, which simplifies to 1/4. With replacement, the jar’s composition stays the same for every draw, so this probability remains constant. Therefore, the correct probability is one quarter. The other fractions would imply a different number of blue marbles than are actually in the jar (for example, 3/20 would require only three blue marbles, and 1/5 would correspond to four blue marbles, etc.).