Question

In a bag, there are 10 marbles, and 4 of them are red.

a. If one marble is drawn from the bag, what is the probability that it will be red?
b. Write the complement of the event in (a) and state its probability.

Answer 1

The probability of drawing a red marble from a bag with 4 red and 6 other marbles is 4/10 or 40%, and the complement probability of drawing a non-red marble is 6/10 or 60%. In different scenarios where marbles are drawn with or without replacement, probabilities change depending on whether the setup is altered after each draw.

Step-by-step explanation:

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In the scenario where a bag contains 4 red marbles and 6 other marbles (which we assume to be non-red for this problem), drawing one marble at random gives us:

1. a. The probability of drawing a red marble would be 4 out of 10, or 40%.
2. b. The complement of drawing a red marble would be drawing a marble of any other color. Since there are 6 marbles that are not red, the probability of not drawing a red marble would be 6 out of 10, or 60%.

Now, considering another scenario based on the provided information:

• If Maria draws a marble and it's blue, then the probability in the first draw is 4 out of 7.
• After drawing a blue marble without replacement, there would be 3 blue marbles left. On the second draw, the probability of drawing another blue marble would then be 3 out of 6.

For James, who replaces the marble each time, the probability remains the same on each draw since the number of each color of marbles does not change.