In the image, an Euler diagram is shown for random events A and B in some random experiment. In each of the four regions, the probability of the corresponding event is indicated. Calculate the probability of the union of events A and B.

Solution:

• The Euler diagram shows the probabilities of different event combinations.
• The probability of event A is the sum of the probabilities in the regions belonging to A: P(A) = 0.4 + 0.2 = 0.6.
• The probability of event B is the sum of the probabilities in the regions belonging to B: P(B) = 0.3 + 0.2 = 0.5.
• The probability of the intersection of events A and B is P(A ∩ B) = 0.2.
• The probability of the union of events A and B is calculated using the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• Substituting the values: P(A ∪ B) = 0.6 + 0.5 - 0.2 = 0.9.
• Alternatively, the probability of the union can be found by summing the probabilities of all regions within A or B: P(A ∪ B) = 0.4 + 0.2 + 0.3 = 0.9.

Answer: 0.9