Calculate the probability

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Calculate the probability that Jupiter will graduate:

10:1 against, I'd say.

I'm sorry. I agree with you. This question is asked by my foriegn friend. And what we students, Chinese students, had ever learned last term is only about calculating probability without replacing after each draw. And I search the knowledge about calculating the probility considering replacing in our native web. But almost the knowledge is just calculating probability without replacing. So I want to ask other country student for help. You're right, my friend doesn't do well in this subject. Actually,last term, I got 93 pionts. But we just learned about calculating the probability without replacing. I'm so sorry.

Surely it's obvious that with replacement, the probability at each draw is the same as that at the first draw without replacement?

I think so too. But I am not sure. I will ask my techer tomorrow because it is 2:00 a.m. now. Thank you.

If you toss an unbiased coin 10 times and it comes up heads every time, what's the probability that the next toss will be a head?

It's 0.5 because each toss is an independent event.

Exactly.

Okay, you're showing some initiative here so I will give you a hint. There is a mathematical reason that a probability of 1 means a certainty it will happen and a probability of 0 means it won't happen.

In my opinion, if we did not replace after each draw, for example, the answer of ii should be:

P (B) = 4/20=0.25

P(BR)= P(B)x P(R)=(4/20)X(6/20)=0.06

P=P(R|B)= P(RB)/P(B)=0.24

but when considering replacement, it should be:

P=P(BR)= P(B)x P(R)=(4/20)X(6/20)=0.06

Don't just memorize formulas. Take time to understand why the probabilities are calculated the way they are. If you understand what you are doing, then you can go from "replacing" to "not replacing", or whatever other version of the problem you need to deal with.

Yeah, you're right. It's a good method to learn everything by understanding instead of rote. Thanks for telling me about these.