Question Video: Applying the Multiplication Rule to Calculate Probabilities | Nagwa Question Video: Applying the Multiplication Rule to Calculate Probabilities | Nagwa

# Question Video: Applying the Multiplication Rule to Calculate Probabilities Mathematics • Third Year of Secondary School

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For two events π΄ and π΅, P(π΅β²) = 0.3 and P(π΄ β£ π΅) = 0.3. Determine the probability of π΄ β© π΅

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### Video Transcript

For two events π΄ and π΅, the probability of π΅ prime equals 0.3 and the probability of π΄ given π΅ equals 0.3. Determine the probability of π΄ intersection π΅.

The first thing to note in this question is weβre not given the probability of π΅, but instead weβre given the probability of π΅ prime. This refers to the complement of π΅, and itβs essentially the probability of π΅ not occurring. As we know all probabilities sum to one, then this means that the probability of π΅ is equal to one subtract 0.3, and thatβs 0.7. Weβre given the probability of π΄ given π΅ as 0.3, and we need to find the probability of π΄ intersection π΅.

We can use the formula for conditional probability that tells us that the probability of π΄ given π΅ is equal to the probability of π΄ intersection π΅ divided by the probability of π΅. As we want to find the probability of π΄ intersection π΅, we can rearrange this formula to help us. Plugging the values into the formula, the probability of π΄ given π΅ is 0.3 and the probability of π΅ is 0.7, so we multiply those together, which gives us the answer that the probability of π΄ intersection π΅ is 0.21.

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