Question

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

There are 4 red, 3 green, 2 blue, and 1 purple marble. So total marbles \( n = 4 + 3 + 2 + 1 = 10 \).

Step2: Probability of drawing a red marble

The number of red marbles \( r = 4 \). Probability \( P(\text{red})=\frac{\text{Number of red marbles}}{\text{Total number of marbles}}=\frac{4}{10}=\frac{2}{5} \).

Step3: Probability of the complement event

The complement of an event \( A \) is \( 1 - P(A) \). So \( P(\text{complement}) = 1 - \frac{2}{5}=\frac{3}{5} \).

Answer:

Probability of drawing 1 red marble: \(\frac{2}{5}\)
Probability of the complement: \(\frac{3}{5}\)