Multiplication Rule and Conditional Probability

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Presentation transcript:

Multiplication Rule and Conditional Probability

Multiplication Rule 1/6 * 4/52 = 4/312 = 1/78 If two events are independent (one event has no impact on the other event): P(AB) = P(A) * P(B) Probability I will roll a 3 and probability I will choose a King from the deck of cards: 1/6 * 4/52 = 4/312 = 1/78

Some other Examples… 1. Choosing a red card and flipping tails. 2. Getting an A and rolling a number greater than 4. 3. Choosing a black face card and flipping heads and rolling odds. 1. 1/2 * 1/2 = 1/4 2. 1/5 * 2/6 = 2/30 = 1/15 3. 6/52 * 1/2 * 1/2 = 6/208 = 3/104

Conditional Probability You use this when you want to show the probability of two events happening in sequence. This is written as P(B|A) (Which is read as Probability of B, given A) What is the probability that you choose a King, given the fact that you have already chosen a Queen of Clubs and not replaced it? Since there are 4 Kings, the top number is 4, but since the queen has been taken out and not replaced, the bottom number is 51. The answer is 4/51.

Another example What is the probability that you choose another Ace, given the fact that you have just chosen the Ace of Spades and not replaced it. Since you just chose the Ace of Spades and now you want the another ace, there are only 3 Aces left: 3 is in numerator. And there are only 51 cards left: 51 is in the denominator. Answer is 3/51 or 1/17.

Multiplication Rule, Continued For example, you want the probability of choosing two aces in a row: 4/52 * 3/51 = 12/2652 or 1/221 If two events are dependent (one event does have an impact on the other event) and the probability they will occur in sequence: P(AB) = P(A) * P(B|A)

Group Work Come up with 2 examples of multiplication rule (independent) and 2 examples of multiplication rule (dependent: Conditional) and give to another group to solve.