# 6th Grade - Probability Of Two Events

 Grade Level: 6th Skill: Probability Topic: Probability of Two Events Goal: Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities. Skill Description: Understand that probability of a combination of two separate, disjoint, events can be found by adding up the individual probabilities. Understand that mutually exclusive, or disjoint, events are two events that cannot happen at the same time. Disjoint events are based on events happening in the same trial. Know how to find the sum of two separate probabilities to name a unified probability. Understand that when independent trials are conducted, one event does not affect the outcome of the second, same event. Know how to find the probability of two independent events by multiplying the probabilities of the separate events. Independent events are based on two trials or more. Identify disjoint events and independent events. Calculate the probability of two disjoint events by adding the probabilities. Calculate the probability of two independent events by multiplying the probabilities.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Identify the two events the disjoint events. There are six cards with the numbers 1 – 6 on each card. One card is drawn at a time. A) A number less than 4 and even is drawn. B) A number less than three is drawn and a number greater than 4 is drawn. (The events in B are disjoint, because these events cannot happen at the same time.) (2) Identify the independent events. There are six cards with the numbers 1 – 6 on each card. One card is drawn, a 5 and the card is put back into the pile. The cards are shuffled. A card is chosen again, it is 7. One card is drawn, a 4. The 4 is placed in the trash. A second card is drawn, a 2. (The events in A are independent, because the first outcome did not affect the second outcome when the card was replaced.) (3) There are six cards with the numbers 1 – 6 on each card. What is the probability that you will draw a prime number or a multiple of 6? Remember, if these events cannot happen at the same time, they are disjoint. Identify the kind of events described. Explain. (4/6 or 67%, disjoint events, same trial) (4) You are conducting an experiment. There are six cards with the numbers 1 – 6 on each card. What is the probability that you will roll a 4 on your first try and a 6 on your second try? Identify the kind of events described. Explain. (1/36 or about 2.7%, independent events, two trials) (5) Determine if the event is disjoint. Explain. There are six cards with the numbers 1 – 6 on each card. What is the probability that you will pull an even number or a multiple of 3? (These events are not disjoint, they have some overlapping favorable outcomes. For example, 6 is both even and a multiple of 3.)

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