Question Video: Determining the Probability of Difference between Two Events Mathematics

Suppose π΄ and π΅ are two events. Given that π(π΄) = 0.3 and π(π΄ β© π΅) = 0.03, determine π(π΄ β π΅).

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Video Transcript

Suppose π΄ and π΅ are two events. Given that the probability of π΄ is equal to 0.3 and the probability of π΄ intersection π΅ is 0.03, determine the probability of π΄ and not π΅.

If we think about these events in a Venn diagram, the probability of π΄ intersection π΅ would be this space, the space for π΄ which does not include the intersection. This is the space when only event π΄ occurs. Another way to say that would be event π΄ minus event π΅. Since we know that the intersection of π΄ and π΅ is 0.03, we can make the statement that the probability of π΄ minus π΅ plus the probability of π΄ intersection π΅ will be equal to the whole probability of π΄.

This means the probability of π΄ minus π΅ plus 0.03 must be equal to 0.3. If we subtract 0.03 from both sides of our equation, we get that the probability of π΄ minus π΅ will be equal to 0.27. This makes sense because 0.27 plus 0.03 does equal 0.3.

The probability of π΄ minus π΅ is the probability that only event π΄ occurs and event π΅ does not occur, and under these conditions that would be 0.27.