Final answer:
The probability of picking a red marble is 1/5. To convert this probability to odds, which are a ratio of favorable to unfavorable outcomes, we take the total probability of picking a red versus not a red marble. Hence, the odds are 1:4, meaning there are four times more chances of not picking a red marble than picking one.
Step-by-step explanation:
The question relates to the concept of probability in mathematics. Specifically, it deals with the probability of picking a red marble from a bag and converting this probability into odds. Probability is the measure of the likelihood of an event happening, expressed as a fraction or a percentage, while odds provide a ratio of the occurrence to the non-occurrence of an event.
To calculate the odds of picking a red marble, given that the probability is 1/5, we need to consider the number of ways the event can happen versus the number of ways it will not happen. There are 3 red marbles initially, and the probability is the number of red marbles over the total number of marbles. In odds, this would be expressed as the number of red marbles over the number of not-red marbles. Given the probability of 1/5, there are 4 not-red outcomes for every red outcome, so the odds are 1:4.
This understanding is built upon scenarios where marbles are drawn from a bag such as the example where a bag contains four blue and three white marbles. If we were to calculate the odds of drawing a blue marble in this case, given that there are 4 blue marbles, we would say the odds of drawing a blue marble are 4:3, because there are three non-blue (white) marbles.