Suppose that, for students who are enrolled in college algebra, 72 percent are freshman, 40 percent...

Suppose that, for students who are enrolled in college algebra, 72 percent are freshman, 40 percent are female, and 25 percent are female and freshman. Your answers should be entered as decimals and rounded to three decimal places.

(A) one student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)? ___

(B) one student will be selected at random. What is the probability that the selected student will not be a freshman? ___

(C) two students will be independently selected at random. What is the probability that both of the selected students will be female? __

Solutions

Expert Solution

P[ students are freshman ] = 72% = 0.72

P[ students are female ] = 40% = 0.40

P[ students are freshman and female ] = 25% = 0.25

(A) one student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)?

P[ student will be a freshman or female (or both) ] = P[ students are freshman ] + P[ students are female ] - P[ students are freshman and female ]

P[ student will be a freshman or female (or both) ] =0.72 + 0.4 - 0.25

P[ student will be a freshman or female (or both) ] = 0.87

P[ student will be a freshman or female (or both) ] = 87%

(B) one student will be selected at random. What is the probability that the selected student will not be a freshman?

P[ students will not be freshman ] = 1 - P[ students are freshman ]

P[ students will not be freshman ] = 1 - 0.72

P[ students will not be freshman ] = 0.28

P[ students will not be freshman ] = 28%

(C) two students will be independently selected at random. What is the probability that both of the selected students will be female?

P[ both will be female ] = P[ students are female ]*P[ students are female ]

P[ both will be female ] = 0.4*0.4

P[ both will be female ] = 0.16

P[ both will be female ] = 16%

orchestra answered 11 months ago

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