The multiplication rule of probability states that the probability of occurrence of both events X and Y are equal to the product of the probability of event Y occurring and the conditional probability that event X occurs when Y occurs.Probability of drawing ace of spades and a heart of card = 1/52 x 13/51 = 1/204. Therefore, the probability of drawing a card of heart = 13/51 Therefore, only 51 cards remain in the deck. Since the ace of spades has already been drawn and replacement is not allowed. Therefore, the probability of drawing ace of spades = 1/52 Since the cards are drawn without replacement, therefore, both the events are dependent upon each other.Īs we know, there is only one ace of spades in a deck of cards. What is the probability of getting an ace of spade, and a card of heart, as first and second card, respectively? Therefore, probability of drawing other pink ball = 11/17īy multiplication rule, P (A ∩ B) = P (A) x P (A|B)Įxample 2: - A magician takes out two cards from a deck of cards, one after the other, without replacement. Since the replacement is not allowed, and the first ball has been drawn, the remaining pink balls in the urn are 17, out of which 11 are pink balls.
The probability of drawing the first ball pink = 12/18 Then, we need to find the probability of P (A ∩ B). Let us assume, A and B be the probability of drawing the first ball pink and the second ball also pink, respectively. What is the probability that both balls drawn are pink? Without replacement, two balls are drawn one after another. Here are the two examples based on the general rule of multiplication of probability-Įxample 1: - An urn contains 12 pink balls and 6 blue balls. One has to apply a little logic to the occurrence of events to see the final probability. One can use this rule for finding probabilities of both independent and non-independent events. Multiplication Rule of Probability: Using General Rule Since X and Y are independent events, therefore,įrom this, we can conclude that the multiplication theorem is true.Įxample: If the probability of getting a red ball is 5/6 and the probability of getting a green ball is 5/7, then the probability of both the events happening at the same time is given by, The multiplication theorem of probability states that if two independent events, X and Y, occur in a random experiment, the probability of simultaneous occurrence of two separate events will be equal to the product of their probabilities.Īlso, we know from multiplication rule that P (X ∩ Y) = P (X) × P (Y|X) One can follow the same rule to find the probability of more than three events.įrom the above multiplication rule of probability, we know The above result is known as the multiplication rule of probability.įor two independent events X and Y, equation (2) can be modified as-įor more than two events X, Y, and Z, multiplication rule of probability is given by. Multiplication Theorem on Probability Video Explanationįrom the multiplication theorem of probability, we know that the conditional probability of occurrence of an event X after event Y has occurred is P (X|Y) and is given by. Multiplication Theorem of Probability Video Explanation Buying a coffee and then buying a pencil.
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