Question

12 fill in the blank 8 points a box contains 5 purple marbles, 3 green marbles, and 2 orange marbles. two consecutive draws are made from the box without replacement of the first draw. find the probability of each event. write your answer as a fraction, decimal, or percent. round 2 decimal places. a. p(orange first, green second) type your answer... b. p(both marbles are purple) type your answer... c. p( the first marble is purple, and the second is any color except purple) type your answer...

Explanation:

Part a: P(orange first, green second)

Step1: Find total marbles

Total marbles = \( 5 + 3 + 2 = 10 \).

Step2: Probability of orange first

Number of orange marbles = 2. So, \( P(\text{orange first}) = \frac{2}{10} \).

Step3: Probability of green second (without replacement)

After drawing an orange marble, total marbles left = 9. Number of green marbles = 3. So, \( P(\text{green second} | \text{orange first}) = \frac{3}{9} \).

Step4: Multiply the probabilities

\( P(\text{orange first, green second}) = \frac{2}{10} \times \frac{3}{9} = \frac{6}{90} = \frac{1}{15} \approx 0.07 \) (rounded to two decimal places).

Step1: Total marbles initially

Total marbles = \( 5 + 3 + 2 = 10 \).

Step2: Probability of purple first

Number of purple marbles = 5. So, \( P(\text{purple first}) = \frac{5}{10} \).

Step3: Probability of purple second (without replacement)

After drawing a purple marble, total marbles left = 9. Number of purple marbles left = 4. So, \( P(\text{purple second} | \text{purple first}) = \frac{4}{9} \).

Step4: Multiply the probabilities

\( P(\text{both purple}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \approx 0.22 \) (rounded to two decimal places).

Step1: Total marbles initially

Total marbles = \( 5 + 3 + 2 = 10 \).

Step2: Probability of purple first

Number of purple marbles = 5. So, \( P(\text{purple first}) = \frac{5}{10} \).

Step3: Probability of non - purple second (without replacement)

After drawing a purple marble, total marbles left = 9. Number of non - purple marbles = \( 3 + 2=5 \). So, \( P(\text{non - purple second} | \text{purple first}) = \frac{5}{9} \).

Step4: Multiply the probabilities

\( P(\text{purple first, non - purple second})=\frac{5}{10}\times\frac{5}{9}=\frac{25}{90}=\frac{5}{18}\approx0.28 \) (rounded to two decimal places).

Answer:

\( \frac{1}{15} \) or approximately \( 0.07 \)

Part b: P(both marbles are purple)