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Chapter 4: Problem 25

A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is a. red? b. green?

Short Answer

Expert verified
The probability of drawing a red marble is 0.45, while the probability of drawing a green marble is 0.55.

Step by step solution

01

Definition of Probability

The key to solving this problem is the definition of probability. The probability P of an event E occurring is calculated by the number of ways E could occur, divided by the total number of possible outcomes. In mathematical terms: \(P(E) = \frac{{\text{{Number of favorable outcomes}}}}{{\text{{Total number of outcomes}}}}\)
02

Calculate Probability of Red Marble

Using the definition of probability, calculate the probability of drawing a red marble. The number of favorable outcomes is the number of red marbles: 18. The total number of outcomes is the total number of marbles: 40. Thus, the probability \(P(Red)\) is calculated as: \(\frac{18}{40}\), which simplifies to \(0.45\) when you divide 18 by 40.
03

Calculate Probability of Green Marble

Similarly calculate the probability of drawing a green marble. There are 22 green marbles, so the number of favorable outcomes is 22 and the total number of outcomes remains 40. Hence, the probability \(P(Green)\) can be calculated as: \(\frac{22}{40}\), which simplifies to \(0.55\) when you divide 22 by 40.

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