Consider a random experiment of tossing a fair coin 5 times in a row. Let H and T denote the events that the coin lands head and tail, respectively. Let A be event of getting heads on the first three tosses. Which of the following is incorrect? A) event a= [HHHHH, HHHHT HHHTH, HHHTT] B) event a’ has total of 12 outcomes C) P(A) = 1/8 D) each outcome in event A has an equal probability of 1/32

One hundred college seniors attending a career fair at a univerisity were categorized according to gender and according to primary career motivation table below shows the results. If one of these students is to be selected at random, find the probability that the student selected will be a female.                  Money    Allowed to be      Sense of      Total                                  Creative              Giving to                                                                   Society   Male           14                5                        11              30 Female        2                35                        33              70 Total           16               40                        44            100 The probability of the student at the fair being female is _______. (Simplify your answer. Type an interger or a fraction.)

Consider the experiment of selecting three balls from a group of 6 yellow, 4 red, and 4 blue balls. Assume the selection is done in order, one after the other, without replacement. Let the random variable x be the number of blue balls among the three balls selected. a) Complete the probability distribution for x x 0 1 2 3 P(x)

1.Suppose a fair coin and a fair die is tossed and A is an event that an even number and a tails appear, what is the number of outcomes in A? 2.Let X be a random variable that denotes the number of heads which appear in tossing a coin twice. Which of the following cannot be a value of the random variable X?

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting an ace or two. ​(b) Compute the probability of randomly selecting an ace or two or six. ​(c) Compute the probability of randomly selecting a five or club. a. ​ P(ace or two​)=nothing ​(Round to three decimal places as​ needed.) b. ​ P(ace or two or six​)=nothing ​(Round to three decimal places as​ needed.) c. ​ P(five or club​)=nothing ​(Round to three decimal places as​ needed.)

We are going to flip a fair coin (heads or tails with equal chance) 3 times, and record the outcome of each flip (H or T). Let event A be the event that there are 2 heads among the 3 flips. What is the event of AC (the complement of event A)? {TTT} {HHT, HTH, THH} {HHH, HTT, TTH, THT, TTT}. O {HTT, THH, HTH, TTT}

An experiment consists of first rolling a dice then tossing a coin: a) How many elements are in the sample space? =8 b) Let A be the event that either a 3 or a 4 is rolled, followed by landing a head on the coin toss. P(A)=  Decimal to 4 places c) Let B be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are events A and B exclusive?