Question Video: Using the Addition Rule to Determine the Probability of Union of Two Events Mathematics

Denote by 𝐴 and 𝐵 two events with probabilities 𝑃(𝐴) = 0.2 and 𝑃(𝐵) = 0.47. Given that 𝑃(𝐴 ⋂ 𝐵) = 0.18, find 𝑃(𝐴 ⋃ 𝐵).

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Video Transcript

Denote by 𝐴 and 𝐵 two events with probabilities the probability of 𝐴 is 0.2 and the probability of 𝐵 is 0.47. Given that the probability of 𝐴 intersection 𝐵 is 0.18, find the probability of 𝐴 union 𝐵.

In order to answer this question, we recall the addition rule of probability, which links all four of these events. This states that the probability of 𝐴 union 𝐵 is equal to the probability of 𝐴 plus the probability of 𝐵 minus the probability of 𝐴 intersection 𝐵. Substituting in the values from this question, we have the probability of 𝐴 union 𝐵 is equal to 0.2 plus 0.47 minus 0.18. This is equal to 0.49. It is important to note that we could also represent this using Venn diagrams, as shown.

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