Question Video: Determining the Probability of Union of Two Mutually Exclusive Events | Nagwa Question Video: Determining the Probability of Union of Two Mutually Exclusive Events | Nagwa

Question Video: Determining the Probability of Union of Two Mutually Exclusive Events Mathematics • Second Year of Secondary School

Two mutually exclusive events 𝐴 and 𝐵 have probabilities 𝑃(𝐴) = 1/10 and 𝑃(𝐵) = 1/5. Find 𝑃(𝐴 ⋃ 𝐵).

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Video Transcript

Two mutually exclusive events 𝐴 and 𝐵 have probabilities the probability of 𝐴 equals one-tenth and the probability of 𝐵 equals one-fifth. Find the probability of 𝐴 union 𝐵.

These two events are mutually exclusive, and so we can recall the addition rule. The probability of 𝐴 union 𝐵 is the sum of the individual probabilities. It’s the probability of 𝐴 plus the probability of 𝐵. For this question then, we have that the probability of 𝐴 union 𝐵 is one-tenth plus one-fifth. We write that fraction of one-fifth as an equivalent fraction with the denominator of 10. It’s two-tenths. And then summing the two probabilities gives three-tenths. By applying the addition rule for mutually exclusive events then, we found that the probability of 𝐴 union 𝐵 is three-tenths.

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