A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Blue 2 is one of the outcomes in which of the following events?Select all correct answers. Select all that apply: B AND O R OR E E′ B′ R AND E O′ B AND E

Suppose that a certain college class contains 59 students. Of these, 30 are freshman, 36 are biology majors, and 5 are neither. A student is selected at random from the class. Given that the student selected is a freshman, what is the probability that she is also a biology major? Write your answer as a fraction.

Please answer and fully explain.

fair die is rolled three times. A 5 is considered "success," while all other outcomes are "failures." Find the probability of 2 successes. The probability of 2 successes is (Type an integer or a simplified fraction.) ...

30% of students take Physics101 and 20% take Math146. Of the students who take Physics 101, 25% also take Math146. The events taking Physics 101 and Math146 are O a. independent O b. dependent O c. Disjoint d. None of the above

There are 7 streets to be named after 7 tree types. Ash, Birch, Cedar, Elm, Fir, Maple, and Willow. A city planner randomly selects the street names from the list of 7 tree types. Compute the probability of each of the following events. Event A: The first three streets are Willow, Cedar, and Birch, without regard to order. Event B: The first street is Cedar, followed by Willow and then Ash. Write your answers as fractions in simplest form. P(1) = 0 P(B) = [

Keno is a casino game in which the player has a card with the numbers 1 through 80 on it. The player selects a set of k numbers from the card, where k can range from one to ifteen. The “caller” announces twenty winning numbers, chosen at random from the eighty. The amount won depends on how many of the called numbers match those the player chose. Suppose the player picks ten numbers. What is the probability that among those ten are six winning numbers?

Alice has a garden containing 9 carnations, 12 roses, and 6 dahlias. Alice randomly selects 6 of these flowers to give to her math teacher. Let X = the number of the selected flowers which are roses.a. a) How many possible ways are there to select the 6 out of 27 flowers (order does not matter) without replacement? b. What is the probability that X = 6 c. What is the probability that X=3? d. What is the probability that X > 3? e. What is the expected value of X? f. What is the standard deviation of X? g. What is the probability that X is within 1.0 standard deviation of its expected value? h. What is the probability that X = 2.6667? Add any comments below.