To calculate the odds of a chain of events, multiply the events' probabilities together. Since we want the lightning to strike any rod target on the first bolt, our odds of success are . The next bolt cannot hit the non-rod target nor the target that was already struck, so our chances are now . The last bolt cannot strike either of the previous two targets or the ground, so our odds drop further to . Multiply these individual probabilities to get the probability of this chain of events:

To find the odds of a particular chain of outcomes, find the product of the odds of each required step's outcomes.

In this case, we can assume that Connell got the first three questions right (in other words, the order doesn't matter since it doesn't noticeably bias the later results).

So the odds of this are:

The odds of getting a problem wrong with a blind guess, on the other hand, is , so the next seven questions being wrong have an odds of:

Lastly, multiply our two individual probabilities together:

Thus, the odds of getting this exact result are 

This is a probability problem.  What you must first decide is what is the probability of getting the outcome you want?  

The probability of getting tails on each of the three coins is  or . 

Since we have three coins, we multiply their individual probabilities to get the final answer:  

 .

To find probability, you must take the # of desired outcomes divided by the total. Thus,

Probabilities can be found by the following equation:  , where the total outcomes is the sum of all of the different number of pets, and the numinator is the number of pets we want to pick (there are only  cats).  In our case, the probability is simply .

This is a combination problem. The solution to the question can be found by considering how many dogs can win the first prize (all five of them)! Then, if one has already won a prize, how many can win the second prize (four). This is because one of the five dogs has already been awarded a prize. Then, how many options are left to win the third prize? The answer is three. In a combination problem, we always multiply all of the possible outcomes for the results to get a total possible outcome value:  

Consider first all of the possible ways the men may be arranged, which is

Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:

1. A G _ _
2. G A _ _
3. _ A G _
4. _ G A _
5. _ _ A G
6. _ _ G A

As seen, there are six possibilities.

Finally, for each of these cases, Craige and Boone could be seated in one of two ways.

So the probability that Aaron and Gary will be seated beside each other is:

243 applicants did not get a scholarship. This ratio is 9:243, which reduces to 1:27.

Probability is the likelihood that an outcome will occur, and it is calculated by dividing the number of favorable events by the total number of possible events that may occur. In order to answer the question, we need to divide the number of non-red and non-blue marbles (i.e. the number of favorable events) by the total number of marbles in the bag (i.e. the total number of possible events). The total number of non-red, non-blue marbles is the same as the number of yellow and green marbles

If the flowers that go in the first two locations are already determined, there are only three positions that run any risk of having the wrong flower planted in them. First, determine the number of possible ways in which Caroline can finish planting the garden. There are 3 possible flowers that she could plant in the third position. After she plants a flower there, there will be 2 flowers she can plant in the fourth position. After planting a flower in the fourth position, there will be only one flower left to plant in the fifth position; therefore, the number of possible ways she could finish the garden is:

There are 6 possible outcomes. Only one of these outcomes will be successful; thus, the probability that Caroline finishes planting the garden in the correct order is one out of six: