Question

pre-algebra ic sem 2 fall 2025
understanding probability
determining the complement
what is the probability of drawing 1 red marble out of a bag
containing 4 red marbles, 3 green marbles, 2 blue marbles,
and 1 purple marble?
what is the probability of the complement of this event?

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(4 + 3+2 + 1=10\)

Step2: Calculate probability of drawing a red marble

Probability of red \(P(R)=\frac{\text{Number of red marbles}}{\text{Total marbles}}=\frac{4}{10}=\frac{2}{5}\)

Step3: Use the complement rule

The complement rule is \(P(\text{not }A)=1 - P(A)\). Let \(A\) be the event of drawing a red marble. Then the probability of the complement \(P(\text{not }R)=1-\frac{2}{5}\)

$$1-\frac{2}{5}=\frac{5 - 2}{5}=\frac{3}{5}$$

Answer:

The probability of drawing a red marble is \(\frac{2}{5}\), and the probability of the complement (not drawing a red marble) is \(\frac{3}{5}\)