The chance of an accident is dependent on the weather conditions, so that is the first branch on the tree diagram.

The probabilities at the next branch are conditional and the last two branches have the chance of accident.

  and ,

so the total probability of an accident is .

The conditional probability formula is the probability of both events happening divided by the probability of the given event.  The probability of saying "yes" and also being a boy is .  The probability of being a boy in the sample is .  So  =  = .

The probability of any event occurring is the number of outcomes in which case that event occurs divided by the number of total number of outcomes.  Here you know that the total number of brown horses is 7, and if 5 of those brown horses are female then 2 must be male. So the probability that a brown horse is male is 2/7.

This question asks for the probability of an event given that one event has occurred, meaning it is a conditional probability. The equation for a conditional probability is:

It is important to properly assign the A and B variables according to the question. It helps to read the equation out loud: "The probability of A given B equals the probability of A and B divided by the probability of A."

We need to find the probability of a female given that the horse is white. Therefore, female horse is A, white horse is B.

So, find each probability needed for the equation.

If 6 of the 7 females are brown, then 1 horse out of 10 is a white female horse.

Now, use the information to solve the equation.

Alternatively you could simply count out the number of favorable outcomes: there are 6 total female horses and 5 are brown, so that leaves 1 white female horse (the "favorable outcome" here). And there are 3 total white horses.  So if you know that you're selecting from the pool of 3 white horses and only 1 is female, the probability of choosing a female white horse from that set is 1/3.

By definition, a discrete random variable is a random variable whose values can be "counted" one by one. A continuous random variable is a random variable that can take any value on a certain interval. Of these choices, the number of lip products, the amount of money, and the number of midterms taken are all discrete random variables, as the respective values can be counted; however, the time taken to watch the first four seasons of a TV show is a continuous random variable, as not everyone will take the same amount of time to watch all those episodes (i.e. some might fastf-orward/replay parts of episodes).

This question pertains to the concept of Geometric Probability Distribution, which states that the probability of  trials until the first success is as follows:

In this equation,  is the probability of success (in this case, a driver caught texting), and  is the probability of failure.

In this particular problem, , and . To calculate the probability of finding that the first driver caught texting is in the thirteenth car stopped, we can calculate . The final answer is .

Two steps are crucial here.

First, we need to recognize this is a binomial distribution with  and .

Second, we need to realize we can use a normal approximation of the binomial since  and , which are both larger than 5.

With that said, we can calculate a -score and its -value, keeping in mind that our mean will be  and our standard deviation will be , which is about .

To calculate Prob(at least one bull's eye), we can instead compute one minus the complementary probability, P(no bull's eye).

So we have P(at least one bull's eye)=1-P(no bull's eye).

The chance of getting no bull's eyes is .

This means the probability of getting at least one bull's eye is 

The movements that this particle can make include: RRL, RLR, LRR.

The chance of getting RRL is . This is also the chance of getting any of those movements.

To get the total probability, we can add up the individual probabilities since the events are all mutually exclusive.

Thus, we get the following as the solution.

To calculate this probability, we need to calculate the chance of getting 4 tails and then a head.

Each tail has a prob. of  and a head is , so we multiply  to the power of 4 (because we need 4 tails) by  (for the single head).

So the probability is 

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