Final answer:
The probabilities of drawing a red, white, and either a yellow or red ball from the jar are 0.2857, 0.4286, and 0.5714, respectively. The probability of at least one person being vaccinated out of three is 0.9148.
Step-by-step explanation:
To calculate the probability of drawing a red ball: P(red) = Number of red balls / Total number of balls. There are 6 red balls and 21 total balls, so P(red) = 6/21, which simplifies to 2/7. When rounded to four decimal places, P(red) = 0.2857.
To find the probability of drawing a white ball: P(white) = Number of white balls / Total number of balls. There are 9 white balls, so P(white) = 9/21, which simplifies to 3/7. When rounded to four decimal places, P(white) = 0.4286.
To calculate the probability of drawing a yellow or red ball: P(yellow or red) = P(yellow) + P(red), as the two events are mutually exclusive. There are 6 yellow balls, so P(yellow) = 6/21, which simplifies to 2/7 (the same as P(red)). When adding the probabilities, P(yellow or red) = 2/7 + 2/7 = 4/7, which equals 0.5714 when rounded to four decimal places.
For the probability of at least one vaccinated person out of three, it's easier to find the complement that none are vaccinated, and subtract from one. If the probability of being vaccinated is 0.56, the probability of not being vaccinated is 1 - 0.56 = 0.44. The probability that all three are not vaccinated is (0.44)^3. Subtract this value from 1 to get the probability that at least one is vaccinated: 1 - (0.44)^3 = 1 - 0.0852 = 0.9148 when rounded to four decimal places.