Question

You toss a coin and roll a die. Find the following probability. Show your work.

P(a tail and a number less than 3)

Answer 1

Are the toss of the coin and the roll of the die dependent or independent events?
That means the following. Is the outcome of the roll of the die influenced by the result of the toss of the coin?

Answer 2

ok

Answer 3

Now try to answer the questions above.
Start with the second question.

Answer 4

After you toss the coin, and you get heads or tails, does that in any way influence what the outcome of the rolling of the die will be?

Answer 5

Yes.

Answer 6

Any thoughts?
Do you understand the question?

Answer 7

Does getting a heads or tails with the coin have anything to do with what you will get after you roll the die?

Answer 8

Im not sure lol.

Answer 9

Ok, thanks for answering.
I'm here to help.
I ask questions to see how much you understand. My goal is to help you, not to put you on the spot.
The tossing of a coin and the rolling of a die are independent events.
That means that the outcome of one event (the tossing of the coin) has no effect at all on the outcome of the other event (the rolling of the coin.)

Answer 10

When you have independent events, you find the probabilities of the two events separately, and then you multiply the two probabilities together to find an overall probability.

Answer 11

What you toss a coin, there are two equally probable outcomes, heads or tails.
The probability of getting tails is: 1/2

When you roll a die, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6, all with the same probability. There are two numbers on a die less than 3: 1 and 2.
The probability of rolling a number less than 3 is the probability of rolling a 1 or a 2:
2/6 = 1/3

The probability of tails followed by a number less than 3 is the product of the probabilities:
1/2 * 1/3 = 1/6

Answer 12

So thats the answer @mathstudent55

Answer 13

Yes.\[\frac{1}{ 2}*\frac{2}{ 6}=\frac{1}{6} \]