Find the probability of the given event. The coin lands heads all five times.

In the game of blackjack, a 2 -card hand consisting of an ace and a face card or a 10 is called a blackjack. a. If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack? b. If a player is dealt 2 cards from 2 well-shuffled standard decks, what is the probability that the player will receive a blackjack?

A halogen desk lamp produced by Luminar was found to be defective. The company has three factories where the lamps are manufactured. The percentage of the total number of halogen desk lamps produced by each factory and the probability that a lamp manufactured by that factory is defective are shown in the accompanying table. What is the probability that the defective lamp was manufactured in factory III? $$ \begin{array}{ccc} \hline & & \text { Probability of } \\ \text { Factory } & \text { Percent of } & \text { Defective } \\ \text { Total Production } & \text { Component } \\ \hline \text { I } & 35 & .015 \\ \hline \text { II } & 35 & .01 \\ \hline \text { III } & 30 & .02 \\ \hline \end{array} $$

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? Four of a kind

In a survey to determine the opinions of Americans on health insurers, 400 baby boomers and 600 pre-boomers were asked this question: Do you believe that insurers are very responsible for high health costs? Of the baby boomers, 212 answered in the affirmative, whereas 198 of the pre-boomers answered in the affirmative. If a respondent chosen at random from those surveyed answered the question in the affirmative, what is the probability that he or she is a baby boomer? A pre-boomer?

The admissions office of a private university released the following admission data for the preceding academic year: From a pool of 3900 male applicants, $40 \%\( were accepted by the university and \)40 \%$ of these subsequently enrolled. Additionally, from a pool of 3600 female applicants, \(45 \%\) were accepted by the university and \(40 \%\) of these subsequently enrolled. What is the probability that a. A male applicant will be accepted by and subsequently will enroll in the university? b. A student who applies for admissions will he accepted by the university? c. A student who applies for admission will be accepted by the university and subsequently will enroll?