Question

instructions: this packet is designed as a rigorous make-up assignment for students who missed the probability test. it is intentionally more challenging and requires mastery of probability concepts. show all work for full credit. express probabilities as simplified fractions, decimals, and percents when applicable. part a: theoretical probability (q1–6) 1. 1. a bag contains 5 red, 4 blue, 3 green, and 2 yellow marbles. one marble is drawn at random. a. find p(red). b. find p(not green). c. express as fraction, decimal, percent.

Explanation:

Part a: Find \( P(\text{red}) \)

Step1: Calculate total number of marbles

Total marbles = Red + Blue + Green + Yellow = \( 5 + 4 + 3 + 2 = 14 \)

Step2: Calculate probability of red

Probability \( P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{5}{14} \)

Step1: Calculate number of non - green marbles

Number of non - green marbles = Total marbles - Number of green marbles = \( 14 - 3 = 11 \)

Step2: Calculate probability of not green

Probability \( P(\text{not green})=\frac{\text{Number of non - green marbles}}{\text{Total number of marbles}}=\frac{11}{14} \)

Step1: Fraction

We already have \( P(\text{red})=\frac{5}{14} \)

Step2: Decimal

To convert fraction to decimal, divide numerator by denominator: \( 5\div14\approx0.357 \)

Step3: Percent

To convert decimal to percent, multiply by 100: \( 0.357\times100 = 35.7\% \)

For \( P(\text{not green})=\frac{11}{14} \):

Step1: Fraction

\( \frac{11}{14} \)

Step2: Decimal

\( 11\div14\approx0.786 \)

Step3: Percent

\( 0.786\times100 = 78.6\% \)

Answer:

\( \frac{5}{14} \) (fraction), approximately \( 0.357 \) (decimal), approximately \( 35.7\% \) (percent)

Part b: Find \( P(\text{not green}) \)