# Video: EG17S1-STATISTICS-Q01

If π΄ and π΅ are two events of a sample space π of a random experiment where π΄ β π΅, then π(π΅/π΄) = οΌΏ. [A] π(π΄) [B] π(π΅) [C] π(π΄ β π΅) [D] π(π)

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### Video Transcript

If π΄ and π΅ are two events of a sample space π of a random experiment where π΄ is a subset of π΅, then the probability of π΅ given π΄ equals blank. Is it a) the probability of π΄, b) the probability of π΅, c) the probability of π΄ minus π΅, or d) the probability of π?

Letβs sketch what we know. If π is our sample space, we have event π΄ which is a subset of event π΅. Weβre looking for the probability of π΅ happening, given that π΄ has happened. We know the probability of π΅ given π΄ equals the probability of the intersection of π΄ and π΅ divided by the probability of π΄. What is the intersection of π΄ and π΅ in our problem?

All of π΄ is the intersection. If the intersection of π΄ and π΅ is the probability of π΄ and we divide that by the probability of π΄, we get one, a probability of one. We donβt see the number one as one of the answer choices. However, one of these probabilities does equal one. We were told that our sample space is π. The probability of the sample space equals one. And that means the probability of π΅ given π΄ is equal to the probability of the whole sample space. At first, this might not seem intuitive to us. So letβs consider an example.

Letβs say our experiment is a fair die roll. And π΄ is rolling a two and π΅ is rolling an even number. In this case, π΄ is a subset of π΅ because two is an even number. What is the probability of π΅ given π΄ for this scenario? Well, itβs the probability that you rolled an even value if you know you rolled a two. And that probability is one. Since π΄ is a subset of π΅ and you know you have π΄, you also have π΅.

The probability of π΅ given π΄ equals one, the probability of the sample space.