Final answer:
To find the probability that a left-handed person has blood group O, we can use Bayes' theorem which calculates this probability based on known conditions. The result is approximately 20.45%.
Step-by-step explanation:
The question is about calculating the probability of a randomly selected left-handed person having blood group O given the various probabilities associated with blood groups and hand orientation. We can use Bayes' theorem to find the required probability. Bayes' theorem helps us find the probability of an event, based on prior knowledge of conditions that might be related to the event.
First, let's define the following:
- P(O) is the probability of having blood group O, which is 30% or 0.30.
- P(Left|O) is the probability of being left-handed given that a person has blood group O, which is 6% or 0.06.
- P(Left|Other) is the probability of being left-handed given that a person has a blood group other than O, which is 10% or 0.10.
- P(O|Left) is the probability of having blood group O given that a person is left-handed, which we are trying to find.
According to Bayes' theorem:
P(O|Left) = [P(Left|O) * P(O)] / [P(Left|O) * P(O) + P(Left|Other) * P(Other)]
Where P(Other) is the probability of having a blood group other than O, which is 1 - P(O) = 0.70.
Now, we calculate P(O|Left):
P(O|Left) = (0.06 * 0.30) / (0.06 * 0.30 + 0.10 * 0.70) = 0.018 / 0.088 = approximately 0.2045 or 20.45%
Therefore, if a left-handed person is selected at random, the probability that he/she will have blood group O is roughly 20.45%.