Basic Math Disjoint Events

Welcome back to Educator.com.0000

For the next lesson, we are going to go over two events that are disjoint.0002

Two events are disjoint when those two events cannot occur at the same time.0009

It can't happen; it is not possible.0017

If we have two events A and B, then the probability or the chance that both are going to occur is 0.0020

That means there is no chance for them to occur together.0030

It is as if I look at my two events, event A occurring, let's say it is that right there.0035

Event B occurring would be like that; they don't overlap.0047

That means they cannot happen together; they cannot occur at the same time.0052

An example of this, if I were to say that right now, it is 5 o'clock pm.0056

It is 5pm; let's say this is A; event A.0075

Event B, if I say it is early in the morning.0083

See how event A, this statement here, it is 5pm, and in statement B, it is early in the morning.0102

They cannot occur at the same time.0110

It is not possible for it to be 5pm and for it to be early in the morning.0112

These two events would be disjoint.0118

These are considered disjoint events because they cannot occur at the same time.0124

They cannot occur together.0130

If I were to say the same statement here, it is 5 o'clock pm.0133

For my second event, my second statement, I am going to say it is dinnertime.0147

This is possible; you can have dinner at 5 o'clock pm.0159

In this case, probability of A and B would be not disjoint because this can occur at the same time.0163

It is not disjoint.0177

If two events cannot occur at the same time, they are disjoint.0180

If they can, then it is not disjoint.0184

Determine if each pair of events is disjoint or not disjoint.0189

The first one, statement A, Samantha is more than 10 years old.0193

That means she could be 11, 12 years old, 13, 20, 30.0202

She is older than 10.0209

Statement B, Samantha is less than 8 years old.0211

She can't be older than 10 and less than 8.0217

This is not possible; this would be disjoint.0221

The second one, the first statement, John is 6 feet tall.0231

For B, John is between 5'10 and 6'2.0240

This is possible; 6 feet is between 5'10 and 6'2; this is not disjoint.0248

The next example, a box weighs 10 pounds.0265

Name a pair of events that would make this statement disjoint and another pair that is not disjoint.0268

We are going to create our own disjoint events and then another pair of events that would be not disjoint.0274

That makes sense; that could occur.0282

The first statement, the one that is disjoint, let's make it that statement right there.0287

A, my first one, a box weighs 10 pounds.0300

For B, our second statement, to make it disjoint, the same box weighs less than 8 pounds.0313

It wouldn't make sense; this is disjoint.0332

For not disjoint, I can say my first statement, a box weighs more than 9 pounds.0339

For my next statement, a box weighs less than 11 pounds.0366

This is true; these two statements are true; it is not disjoint.0381

The third example here, determine if each set of events is independent, dependent, or disjoint.0392

Remember independent events, when we have two events that do not affect each other.0398

The outcome of the second event is not affected or does not depend on the first event.0403

Dependent events are the opposite.0411

The second event is affected by the first event.0414

The probability of the second event occurring is affected or is determined by the outcome of the first event.0419

Disjoint remember is when we have two events that cannot occur at the same time.0713.2.0429

It is not possible for them.0433

The first statement, a person picks a card from a deck of playing cards.0436

Without replacing it, another person picks another card from the same deck.0441

There are 52 cards in a deck; a person picks a card.0449

That is the first event; the first pick is the first event.0455

Without replacing it, another person picks another card from the same deck.0461

For the first event, when you pick a card, it is 1 card out of a total of 52.0470

This is the first event.0483

Then for the second event, for the second pick,0487

since the first card is not replaced back into the deck, there is o1ne card missing now.0491

There is no longer 52 cards.0498

The second person is going to pick 1 card out of a total of 51.0503

1 card out of 52 times 1 card out of 51.0514

Here all we want to know is if the two events together, is it independent, dependent, or disjoint?0518

See how the second event here is affected by this first event because the card was not replaced.0530

It is not put back in; so now there is less cards.0536

The card that the second person picks might be different; it is affected.0539

This would be a dependent event; these are dependent events.0545

The second one, Sarah received 100 percent on her chapter five math test.0556

Sarah failed her chapter five math test.0562

The first event is that she received 100 percent.0565

She got an A plus; nothing wrong.0572

Then the second event, Sarah failed her chapter five math test.0576

If you get 100 percent, is that failing?--no.0584

This event here with this event B here cannot occur at the same time.0588

It is not possible for both to be true.0597

This would be an example of disjoint events.0600

The third one, Susan rolled a number cube and got a 4.0611

She rolled again and got a 3.0615

A number cube is a die; we know that there are 6 sides.0618

Each side has a different number; 1, 2, 3.0626

She rolled a number cube at got a 4.0633

What is the probability of rolling a 4?0637

Desired outcome, how many sides on this number cube is a 4?0641

Only 1 side; that is 1 out of a total of 6 sides.0647

The probability of rolling a 4 is 1/6; that is the first event.0654

She rolled again and got a 3; what is the probability of rolling a 3?0660

How many sides has a 3?--only 1 side out of 6.0669

Here to find the probability of rolling a 4 and then a 3 for those two events is 1/6 times 1/6.0677

See how even though she rolled the first time and got a 4, she rolled again.0691

For the second event, rolling a 3, was that affected by what she got from the first roll?0697

No, just because she rolled a 4 the first time doesn't mean that0704

she can't roll a 4 again on the second time, on the second roll.0707

These two events are independent.0711

This second roll, the second event, is not affected,0722

does not depend on this roll here, the probability of getting the 4.0725

That is it for this lesson; thank you for watching Educator.com.0730