The Multiplication Rule of Probability Explained

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The Multiplication Rule of Probability Explained

Jeremy Blitz-Jones · ⏱ 3:12 · 234.8K مشاهدة · 7 years ago

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what's the chance of rolling Snake Eyes what's the chance of flipping heads three times in row when calculating the probability of two or more events happening together we can use the multiplication rule of probability we'll start with independent events where one events outcome has no effect on the other events outcome for example what's the probability of rolling Snake Eyes each roll is an independent event because the value on one die has no influence on the value of the second die the multiplication rule of probability says that the probability of two events and happening together is the probability of event multiplied by the probability of event in this case the probability of rolling 1 on the first die multiplied by the probability of rolling 1 on the second die this is the case if you're rolling the dice together or one at time the probability of rolling 1 on die is 1 out of 6 so the probability of rolling 1 on both dice is 1/6 times 1/6 or 1 out of 36 across all 36 possible rolls of two dice one of them is Snake Eyes let's look at the second example what's the probability of flipping heads three times in row well it's the probability of the first flip landing heads multiplied by the probability of the second flip landing heads multiplied by the probability of the third flip landing heads one-half times one-half times one-half one-eighth what if the events are dependent what if the second events probability is based on the outcome of the first event in this case the probability of the events happening together is little more complicated the probability of event happening multiplied by the probability of event happening given that event happened for example what's the probability that you'll draw an ace hold on to it and then draw king we'll start with the probability of drawing an ace 4 out of 52 cards or aces then we'll need to calculate the probability of drawing king given that we've already drawn an ace which is different than the probability of drawing king from full deck there are four kings left in the deck and there are 51 cards remaining since we're holding on to an ace we multiply these two probabilities together and we get probability of 16 out of 2652 about 1 in 167 chance in summary if you want to know the likelihood of event and event happening you can use the multiplication rule of probability make sure to identify whether the events are independent or dependent and adjust your calculation accordingly happy probability and thanks for watching interested in other topics let me know in the comments