11-05-2009, 10:31 PM
I'll explain this question by question so you can understand. These formulas will apply throughout and note that I included key words that will tell you when to use them:
probability=# of relevant outcomes/total # of outcomes
probability(and, with replacement)=relevant outcomes/total outcomes x relevant outcomes/total outcomes
probability(and, without replacement)=relevant outcomes/total outcomes x relevant outcomes(-1 if applicable)/total outcomes-1
probability(or)=relevant outcomes/total outcomes + relevant outcomes/total outcomes
1. First we will find the total number of outcomes, which is simply found by adding together all of the cards(32+25=57). Now, the relevant outcomes are 18(Indians) and 10(Bengals). To find the probability of choosing one of each(I'm assuming this is with replacement, so there isn't a missing card afterwards), you simply multiply. So it'd be the second formula from above:
18/57 x 10/57 = 180/3249
I'm figuring you know how to simpify, so I'm not going to explain that.
2. For this one, we are going to use our third formula. We already know from the given information that there are 25 football cards to chose from, so now we need to apply what we know about the types of cards here. The real difference is because we are not replacing a card, that means the number of cards are going to go down to 24 because there is one less possibility(though because we want different types of cards, the top number remains unaffected. If we wanted two bengals cards, it would also go down by 1). So we have:
10/25 x 15/24 = 150/600
3. First, we need to know the total number of outcomes for each roll, which is 8 as we were told. This won't change because we are using two different dies, each with 8 sides that cannot be taken away, so we are going to use formula two. Next, we need to know how many "3"s are on each die, which is 1 for each one. So our formula is:
1/8 x 1/8 = 1/64
4. As always, we determine the formula we are going to use. The keyword is "without replacement", so we will use formula three. Next, we want to find the total number of outcomes:
8 + 12 = 20
Now, we need to put in the relevant outcomes. Since our first pick is blue, the first number will be 8/20, and since the second pick is green, the second number will be 12/19(notice because the item of choice is different so we didn't subtract from the top number; we did for the bottom one though since one is gone from the total). So, our formula is:
8/20 x 12/19 = 96/380
5. This seems confusing, but it really isn't. What we are doing is the same this as above with the second formula, there just are different totals involved(9 and 4, respectively). Since these is only going to be one correct possibility for each, that means the relevant outcome for both is "1". So, our formula is:
1/9 x 1/4 = 1/36
You found this already, but it always helps to go over it again.
The key thing about probability is just understanding what goes where. Its confusing regardless, but you just have to keep going at it. If this doesn't make sense, please ask me to clarify confusing points. Probability is a tough thing to explain.