Independent event and mutually exclusive event

  • Thread starter kingwinner
  • Start date
  • Tags
    Independent
In summary, an independent event is an event that is not affected by the outcome of another event, while a mutually exclusive event cannot occur at the same time as another event. To determine the probability of independent events, you multiply the individual probabilities of each event, while for mutually exclusive events, you add the individual probabilities. Two events cannot be both independent and mutually exclusive, or both dependent and mutually exclusive, as these conditions are contradictory.
  • #1
kingwinner
1,270
0
This is my second class in intro to probability at a university level.

1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10.

a) Now what is P(pick 1 girl and 1 boy) equal to if the order doesn't matter?

b) What is P(pick 1 girl and 1 boy) equal to if the order does matter?
=====================
1a) My guess is that P(pick 1 girl and 1 boy) = 2/5 x 3/4 = 6/20 = 3/10 if the order doesn't matter. Is this right?

1b) No idea...

=======================
2) What is the difference between an "independent event" and a "mutually exclusive event"? I can't visualize the difference...


Can someone help me please?
 
Physics news on Phys.org
  • #2
1a. You made the order matter. Double check your answer: What are the only possible outcomes if you pick 2 people, and order doesn't matter? (Hint: three mutually exclusive events.) The probabilities for these exclusive events had better add to one.

1b. Once you get the answer correct for 1a. you should get this easily.

2. You shouldn't rely on us so much. A quick google search revealed multiple sites that give a very good explanation. A little research on your own part would help you a lot more than us spoonfeeding you the answers.
 
  • #3
1a) (2/5 x 3/4) x 2 = 12/20 = 3/5 ?

1b) 2/5 x 3/4 = 3/10 ?
 
  • #4
You have the correct answers, but by guessing. If order does matter, there are four possible outcomes: <B,B>, <B,G>, <G,B>, and <G,G>. You calculated the probability of the <G,B> outcome correctly in 1b) as 2/5 x 3/4. The probability of the <B,G> outcome is 3/5 x 2/4. The order-insensitive outcome (G,B) is the union of the two mutually exclusive <B,G> and <G,B> outcomes. Adding the probabilities (valid since the events are mutually exclusive), P((G,B)) = P(<G,B>)+P(<B,G>) = 2/5 x 3/4 + 3/5 x 2/4 = 3/5.
 

1. What is the difference between an independent event and a mutually exclusive event?

An independent event is an event whose outcome is not affected by the outcome of another event. In other words, the occurrence or non-occurrence of one event has no impact on the probability of the other event happening. On the other hand, a mutually exclusive event is an event that cannot occur at the same time as another event. If one event happens, the other event cannot happen.

2. How do you determine the probability of independent events?

To determine the probability of independent events, you multiply the individual probabilities of each event. This is known as the multiplication rule. For example, if the probability of event A is 0.5 and the probability of event B is 0.7, then the probability of both events occurring is 0.5 x 0.7 = 0.35.

3. Can two events be both independent and mutually exclusive?

No, two events cannot be both independent and mutually exclusive. This is because if two events are independent, the occurrence of one event does not affect the probability of the other event happening. However, if two events are mutually exclusive, the occurrence of one event makes it impossible for the other event to happen. These two conditions are contradictory and cannot coexist.

4. How do you determine the probability of mutually exclusive events?

The probability of mutually exclusive events can be determined by adding the individual probabilities of each event. This is known as the addition rule. For example, if the probability of event A is 0.4 and the probability of event B is 0.6, then the probability of either event A or event B occurring is 0.4 + 0.6 = 1.0.

5. Can two events be both dependent and mutually exclusive?

No, two events cannot be both dependent and mutually exclusive. If two events are dependent, the occurrence of one event affects the probability of the other event happening. However, if two events are mutually exclusive, the occurrence of one event makes it impossible for the other event to happen. These two conditions are contradictory and cannot coexist.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
691
  • Precalculus Mathematics Homework Help
Replies
24
Views
930
  • Calculus and Beyond Homework Help
Replies
3
Views
865
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
732
  • Calculus and Beyond Homework Help
Replies
16
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
192
  • Calculus and Beyond Homework Help
Replies
1
Views
170
  • Calculus and Beyond Homework Help
Replies
11
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
763
Back
Top