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Compound events example using diagram (mistake in video)
Sal uses a diagram to find the probability of rolling a four-sided die and a six-sided die and not getting a 1. Created by Sal Khan.
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Alright everyone, in not full-screen mode, it corrects Mr. Sal's mistake at about2:00it makes the correction: 'Sal says "3 by 4" but should have said "3 by 5". The probability that neither die shows a 1 is "15/24", which simplifies to "5/8".'
To Khan Academy: please re shoot this video.(23 votes)
Yes, this video needs to be removed, because the correction is not visible unless in minimized view. If students don't go through these question threads, then confusion and errors will result.(5 votes)
In problems like these, is there a way to calculate the answer without having to use the sample space given. If I am taking a timed exam, I wouldn't have time to draw out this sample space. Can anyone suggest me to a video that might teach me how to do this?(7 votes)
To answer the question without drawing each of the possibilities, you can think about it logically. To do this, remember number of favorable outcomes/ number of possible outcomes. In this case, you have a six sided die so you have a total of six possibilities. Then, since you do not want to have a one as a possibility, you subtract 6-1=5 which means you have a 5/6 probability for that die.
If that didn't make as much sense try to think of it like this:
Visualize the six sided die. The possible solutions are 1,2,3,4,5, or 6 that you could roll. The problem tells you that one is not wanted in the solution so 2,3,4,5, and 6 are remaining as the favorable solutions.
After that do the same for the other die. It has 4 total possibilities and a favorable outcome of 3 so it is 3/4.
Then just multiply these two fractions together to get the answer. 5/6 x 3/4(25 votes)
should it not be 15/24 which is 3/8??(0 votes)
was it supposed to be 15\24 not 12\24 ?(3 votes)
Is there a formula for this?(3 votes)- favorable/possible
unless you're talking about the percentage of dogs likely to get fleas when visiting the dog park, then it would be unfavorable/possible
maybe we need a different word there
but that's the basic idea(2 votes)
- the answer s 15/24 not 1/2(3 votes)
- The answer is wrong, it should be 15/24 or 5/8.(3 votes)
- I don't understand why the answer is not 1/24. The constraint, "neither shows a 1", would imply to me that you can't see a 1 on any die after the roll. There is only a 1/6 chance of the 6-sided die hiding its 1 and a 1/4 chance of the 4-sided die hiding its 1. There is only 1/24 outcome where both dice have their 1's face down.(0 votes)
Well, it would imply something different to me. And something different to someone else. That is why in maths we define things so that there are no different interpretations. In this problem, though, they probably though that it was well enough defined.
Otherwise, could you find the solution IF "show a 1" meant having a one in the top?
As long as you agree that the solutions was the one given IF we interpret the question in that way, there should be no problem ((You could however claim that the question is not clear enough as it allows several interpretations)).(5 votes)
Shouldn't the answer be 15/24 because it is 3*5 and not 3*4.(2 votes)
P(Of not having a one when a six sided and four-sided dice were rolled) = 12/24 = 1/2.
How come? I thought it was 15/24 = 5/8(2 votes)
2:00Video transcript
If you roll a six-sided
die and a four-sided die, what is the probability
that neither die shows a 1? The grid below shows all
the possible outcomes of rolling a six-sided
die and a four-sided die. And we're fairly familiar
with six-sided die. Those are the cubes that we're
used to from the board games that we've been playing
our entire lives, that look something like that. And your roll is
whatever is the face up. You're probably less
familiar with four-sided die. These are more like these
triangular pyramids. They look something like this. So it has 1, 2, 3, and then
the one side on the bottom. And here your roll is
actually the face, the side, that is facing the bottom. And so what you have
here is a picture of all the possible rolls. They have the six-sided die, the
side that's facing on the top. And then on the
triangle, this shows what is the result of the
roll of the four-sided die. So this actually would be
the side that's facing down. Let's actually try to
answer their question, because they gave us all of the
possible outcomes of rolling a six-sided die and
a four-sided die. So we want to know,
what is the probability that neither dies shows a 1? So how many total
outcomes do we have? Let's see-- 1, 2, 3,
4 by 1, 2, 3, 4, 5, 6. 4 times 6, that makes sense. There's six possible outcomes
for the six-sided die, four possible outcomes
for the four-sided die. 4 times 6-- so there's 24
total possible outcomes. And then how many
of the outcomes meet our constraint that
neither died shows a 1? So this one. So anything in this
row isn't going to meet our constraint,
because these have a 1 on the four-sided die. And nothing in this
column is going to meet our constraint,
because these have a 1 on the six-sided die. But all of these,
everything left over, these are going to
meet our constraints. These are going to
meet our constraints. And how many of these
outcomes are there? Well, let's see. There's 3 by 4-- 3 times 4. So there's 12 possible
outcomes here. 12/24 is the probability. You could say there's
a 12/24 probability. But if you wanted to write
it as an equivalent fraction that's using lower numbers, this
is the same thing as-- divide the numerator and
denominator by 12-- 1/2. So the probability that
neither die shows a 1 is 1/2.