Probability math question.

Question

bealiberty47 · Answer

attachment

anonymous · Answer

Some questions for you: How many marbles are there in total? How many of them are red? blue?

bealiberty47 · Answer

16 marbles in total
4 red
7 blue

anonymous · Answer

Alright, so the probability of drawing a red is $\dfrac{\text{number of reds}}{\text{total number of marbles}}$. Similarly, the probability of drawing a blue is $\dfrac{\text{number of blues}}{\text{total number of marbles}}$

bealiberty47 · Answer

Red probability is 4/16 simplified to 1/4
Blue probability is 7/16

bealiberty47 · Answer

right?

anonymous · Answer

Yes. So in the first problem, you're drawing a red marble first, which you know has probability 1/4. When you put the marble back in, you still have 16 total marbles, so the probability of drawing a blue is 7/16.

The fact that you replace the first marble means that your draws are independent. This means
$$P(\text{red then blue})=P(\text{red})\times P(\text{blue})$$

bealiberty47 · Answer

so you multiply red, 4, by blue, 7. or you multiply the probabilities of 1/4 and 7/16

anonymous · Answer

You multiply the probabilities. $P(\text{red})=\dfrac{1}{4}$ and $P(\text{blue})=\dfrac{7}{16}$, so $P(\text{red then blue})=\dfrac{1}{4}\times\dfrac{7}{16}$.

bealiberty47 · Answer

sorry was afk my mom called. I'll get right to that :)

bealiberty47 · Answer

7/64?

anonymous · Answer

Right.

For the second problem, you're not putting back the first marble. So on the first draw, the probability of drawing a red stays the same, $\dfrac{1}{4}$.

On the second draw, there are now 15 marbles in total, so what's the probability of drawing a blue from these 15?

bealiberty47 · Answer

7/15

anonymous · Answer

Right. As before, the probabilities are independent, so
$$P(\text{red, then blue (after replacement)}=P(\text{red})\times P(\text{blue})_{\text{(after replacement)}}$$

bealiberty47 · Answer

so 1/4 x 7/15 = 7/60

anonymous · Answer

Yes

anonymous · Answer

The answer to part (c) should be obvious. In the first scenario, you're keeping the number of total marbles the same, but in the second it's being changed.

bealiberty47 · Answer

yeah ok. I get it. I was pretty much speeding through the lesson cause its the end of school but I do enjoy math when I slow down and understand it. Thanks so much :)

anonymous · Answer

You're welcome!