Step-by-step explanation:
If there are 3 red marbles, 5 green marbles, and 2 blue marbles, we can find the probability of finding one of them easily.
1. If we add these numbers up, we get 10, so the red marbles plus the green marbles = 8 and then there are 2 blue ones. This means that there is an 80% chance of pulling a red or a green marble. Number one is correct.
2. The probability of drawing a red marble followed by a green marble depends on each individual probability. For a red marble, that is [tex]\frac{3}{10}[/tex] = 30% chance, and a green marble is [tex]\frac{5}{10}[/tex] = 50% chance. Since we are drawing out of 20 marbles (Two sets of ten), we can conclude that the chances for red are [tex]\frac{6}{20}[/tex]; green's chances are [tex]\frac{10}{20}[/tex], and blue's chances are [tex]\frac{4}{20}[/tex]. Assuming that we draw a red marble first, there is a [tex]\frac{6}{20}[/tex] chance of that. There is a [tex]\frac{10}{20}[/tex] chance of drawing a green, so we can conclude that the probability of drawing a red marble followed by a green marble is [tex]\frac{4}{20}[/tex] ([tex]\frac{10}{20}[/tex] - [tex]\frac{6}{20}[/tex]), witch is not [tex]\frac{1}{6}[/tex]. Number two is incorrect .
3. The probability of drawing a blue marble is 20%, so the probability of not drawing a blue marble is 80%. Number three is incorrect.
4. The probability of drawing a green marble is 50% and the probabilities of red and blue combined are equal to 50% (3 red + 2 blue = 5, and their are 5 green marbles therefore 50 50 chance). Number four is correct.
Answer:
The probability of randomly drawing a red marble(red 3) and then a green (green 5) marble is [tex]\frac{1}{6}[/tex] .
The probability of drawing a green marble is the same as the probability of drawing either a red or a blue marble.
The probability of randomly drawing either a red marble or a green marble is 80%.
