Question Video: Determining the Probability of Union of Two Independent Events

Denote by 𝐴 and 𝐵 two independent events. Given that 𝑃(𝐴) = 0.5 and 𝑃(𝐵) = 0.48, find 𝑃(𝐴 ∪ 𝐵).

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Video Transcript

Denote by 𝐴 and 𝐵 two independent events. Given that the probability of 𝐴 is 0.5 and the probability of 𝐵 is 0.48, find the probability of 𝐴 union 𝐵.

We know that if two events are independent, then the probability of 𝐴 and 𝐵, or 𝐴 intersection 𝐵, is equal to the product of the two events, the probability of 𝐴 multiplied by the probability of 𝐵. In this question, the probability of 𝐴 intersection 𝐵 is 0.5 multiplied by 0.48. 0.5 is the same as a half. And a half of 48 is 24. Therefore, 0.5 multiplied by 0.48 is 0.24.

We have been asked to calculate the probability of 𝐴 or 𝐵, or 𝐴 union 𝐵. In order to do this, we recall the addition rule of probability. 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 we know gives us 0.5 plus 0.48 minus 0.24. 0.5 plus 0.48 is equal to 0.98. Subtracting 0.24 from this gives us 0.74. The probability of 𝐴 union 𝐵 is 0.74.

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