Video: Determining the Probability of an Event Involving Mutually Exclusive Events

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that 𝑃(𝐴′) = 0.61 and 𝑃(𝐴 ∪ 𝐵) = 0.76, determine 𝑃(𝐵).

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Video Transcript

Suppose 𝐴 and 𝐵 are two mutually exclusive events. Given that 𝑃 of 𝐴 dash equals 0.61 and the probability of 𝐴 union 𝐵 equals 0.76, determine the probability of 𝐵.

The probability of 𝐴 dash means the probability of 𝐴 not occurring. This means that the probability of 𝐴 is one minus the probability of 𝐴 dash. Substituting in the value of the probability of 𝐴 dash gives us the probability of 𝐴 is equal to one minus 0.61. As one minus 0.61 is 0.39, the probability of event 𝐴 occurring is 0.39.

If two events are mutually exclusive, the probability of 𝐴 union 𝐵 is equal to the probability of 𝐴 plus the probability of 𝐵, as there is no intersection. Substituting in our values for the probability of 𝐴 and the probability of 𝐴 union 𝐵 gives us the equation 0.39 plus the probability of 𝐵 equals 0.76. Subtracting 0.39 from both sides of this equation gives us a value of 𝐵 of 0.37.

This means that if we have two mutually exclusive events 𝐴 and 𝐵, where the probability of 𝐴 dash is 0.61 and the probability of 𝐴 union 𝐵 is 0.76, then the probability of 𝐵 will be 0.37.

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