(in thousands) shows the number (in thousands) of earned degrees, by level and l

Question

(in thousands) shows the number (in thousands) of earned degrees, by level and l. Center conferred in the United States in a recent year. Aource Us Naional for Education Statistics) Gender Male Female Total Associate's 275 453 728 Level Bachelor's 650 875 1525 of Master's 238 366 604 Degree Doctoral 30 30 60 Total 1193 1724 2917 A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who (a) earned a bachelor's degree. b) earned a bachelor's degree given that the person is a female (c) earned a bachelor's degree given that the person is not a female. (d) earned an associate's degree or a bachelor's degree. (e) earned a doctorate given that the person is a male. earned a master's degree or is a female. (g) earned an associate's degree and is a male. (h) is a female given that the person earned a bachelor's degree. 2. Which event (s) in Exercise 1 can be considered unusual? Explain your reasoning. 3. Decide if the events are mutually exclusive. Then decide if the events are ndependent or dependent. Explain your reason Event A: A golfer scoring the best round in a four-round tournament Event B: Losing the golf tournament 4. A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive (a) no defective units.

Explanation / Answer

Solution

Back-up Theory

Probability of an event E, denoted by P(E) = n(E)/n(S) …………………………(1)

where n(E) = Number of outcomes favourable to the event E and

n(S) = Total number all possible outcomes.

For 2 events, A and B,

P(A B) = P(A) + P(B) - P(A B), in general and ……………………………(2)

P(A B) = P(A) + P(B), ………………………………………………..………(3)

when A and B are mutually exclusive (i.e., A and B have nothing common),..…(4)

Now, to work out solution,

Q1 Part (a)

Probability a randomly selected person earned a bachelor’s degree = Number of persons who earned a bachelor’s degree/Total number of persons who earned a degree = 1525/2917 = 0.5228 ANSWER

Q1 Part (b)

Probability a randomly selected person earned a bachelor’s degree given that the person is female = Number of females who earned a bachelor’s degree/Total number of females who earned a degree = 875/1724 = 0.5075 ANSWER

Q1 Part (c)

Probability a randomly selected person earned a bachelor’s degree given that the person is not female = Number of males who earned a bachelor’s degree/Total number of males who earned a degree = 650/1193 = 0.5448 ANSWER

Q1 Part (d)

Probability a randomly selected person earned an associate’s degree or bachelor’s degree = Probability a randomly selected person earned an associate’s degree + Probability a randomly selected person earned a bachelor’s degree [vide (4) under Back-up Theory]

= (728 + 1525)/2917 = 2253/2917 = 0.7724 ANSWER

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