Question

there are only 2 red marbles in each of these jars.
10 marbles
100 marbles
500 marbles
1000 marbles
without looking in the jars, you are to pick a marble out of one of the jars.
which jar would give you the greatest chance of picking a red marble?
a. the jar with 10 marbles
b. the jar with 100 marbles
c. the jar with 500 marbles
d. the jar with 1000 marbles
e. all jars would give the same chance.

Explanation:

Step1: Recall Probability Formula

The probability of picking a red marble is given by \( P(\text{red})=\frac{\text{Number of red marbles}}{\text{Total number of marbles}} \). Here, each jar has 2 red marbles.

Step2: Calculate Probability for Each Jar

• For Jar A (10 marbles): \( P_A=\frac{2}{10} = 0.2 \)
• For Jar B (100 marbles): \( P_B=\frac{2}{100}=0.02 \)
• For Jar C (500 marbles): \( P_C=\frac{2}{500} = 0.004 \)
• For Jar D (1000 marbles): \( P_D=\frac{2}{1000}=0.002 \)

Step3: Compare Probabilities

We compare \( 0.2, 0.02, 0.004, 0.002 \). The largest probability is 0.2, which corresponds to the jar with 10 marbles.

Answer:

A. the jar with 10 marbles