Suppose George wins 38​% of all thumb wars. ​(a) What is the probability that George wins two thumb wars in a​ row? ​(b) What is the probability that George wins four thumb wars in a​ row? ​(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that George wins four thumb wars in a​ row, but does not win five in a row. ​(a) The probability that George wins two thumb wars in a row is nothing. ​(Round to four decimal places as​ needed.)

A physics class has 50 students. Of these, 11 students are physics majors and 16 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is (Round to three decimal places as needed.) ******************

A math class consists of 15 students, 5 female and 10 male. Three students are selected at random, one at a time, to participate in a probability experiment (selected in order without replacement).(a) What is the probability that a male is selected, then two females?  (b) What is the probability that a female is selected, then two males?  (c) What is the probability that two females are selected, then one male?  (d) What is the probability that three males are selected?  (e) What is the probability that three females are selected?

EXAMPLE 5 If 3 balls are "randomly drawn" from a bowl containing 6 white and 5 black balls, what is the probability that one of the balls is white and the other two black?