A box contains 2 green apples and 2 red apples. Apples are taken from the box, one at a time, withoutreplacement. When both red apples have been taken, the process stops. The random variable X is thenumber of apples which have been taken when the process stops.(i) Show that P(X = 3) =

Use a sample space to determine whether the events are independent. There are three green apples and one red apple in a bowl. You randomly select one apple to eat now and another apple to eat with lunch. Determine whether randomly selecting a green apple first and randomly selecting a green apple second are independent events.

A jar has 13 candies where six of the candies are red, and seven candies are green. Imagine in a first draw, eight candies are randomly picked from the jar. We are interested in the number of green candies in that first draw. Which words clearly define the random variable X here?Question 3Answera.X = the number of green candies in the first draw.b.X = the number of red candies in the first draw.c.X = the number of green and

A wheel has 10 equally sized slices numbered from 1 to 10.Some are grey and some are white.The slice numbered 3 is grey.The slices numbered 1, 2, 4, 5, 6, 7, 8, 9, and 10 are white.The wheel is spun and stops on a slice at random.Let X be the event that the wheel stops on a white slice, and let PX be the probability of X.Let not X be the event that the wheel stops on a slice that is not white, and let Pnot X be the probability of not X. (a)For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Event Outcomes Probability1 2 3 4 5 6 7 8 9 10X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.

Snow White met the old witch who became the evil queen. The old witch had 10 apples in total. Unlike in the fairy tale, this time the old witch asked Snow White to choose which apple to eat. What is the probability that Snow White will eat the poisonous apple?

A fruit basket contains 6 apples, x mangoes, x + 3 guavas. If a fruit is chosen randomly from the basket, then the probability of it being guava is 37 . What is the probability of choosing two fruits from the basket one after the other without replacement, such that the first fruit chosen is a mango and the second fruit chosen is an apple?