Statistics Chapter 5 Quiz 5.2C Answer Key

Quiz 5.2C Statistics Name: ( Suppose you toss one coin and roll one six-sided die. (a) List the outcomes in the sample space. H1 T1 H2 T2 H3 T3 H4 T4 H5 T5 H6 T6 (b) Find the probability of getting a head. 12 outcomes 6 have heads \(P(H) = \frac{6}{12} = \frac{1}{2}\) (c) Find the probability of getting a 1, 2, or 3 on the die. mutually exclusive \(P(1 \text{ or } 2 \text{ or } 3) = P(1) + P(2) + P(3)\) \(P(1 \cup 2 \cup 3) = \frac{2}{12} + \frac{2}{12} + \frac{2}{12} = \frac{6}{12} = \frac{1}{2}\) (d) Find the probability of getting a head or a five. not mutually exclusive \(P(H \text{ or } 5) = P(H) + P(5) - P(H5)\) \(= \frac{6}{12} + \frac{2}{12} - \frac{1}{12}\) \(= \frac{7}{12}\) In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. If a student is selected at random, find the probability of selecting 1   1. mymission.lamission.edu mymission.lamission.edu Males Females total (a) a junior or a female not mutually exclusive table Seniors 6 4 10 Juniors 12 6 18 \(P(J \text{ or } F) = P(Jr) + P(F) - P(JrF)\) \(= \frac{18}{28} + \frac{10}{28} - \frac{6}{28}\) 28 Read 20 28 \(= \frac{24}{28} = \frac{6}{7}\) (b) not a junior male P(not a junior male) = 1 - P(Jr and male) (= 1 - \frac{12}{28}) (= \frac{16}{28}) (= \frac{4}{7}) Consolidated Builders has bid on two large construction contracts. The company president believes that the probability of winning the first contract (event A) is 0.6, that the probability of winning a second (event B) is 0.3, and that the probability of winning both jobs is 0.1. (a) Construct either a Venn diagram or a two-way table that summarizes what you know about events A and B. 1   1. afebles.weebly.com afebles.weebly.com [Venn Diagram] A = 0.5, A ∩ B = 0.1, B = 0.2, Outside = 0.2 [Two-way Table] Event B: Y | N Event A: Y | 0.1 | 0.5 N | 0.2 | 0.2 (b) What is P(A or B) - the probability that Consolidated wins at least one of the job? P(A ∪ B) = 0.5 + 0.1 + 0.2 = 0.8 or P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.6 + 0.3 - 0.1 = 0.8 (c) Write each of the following events in terms of A, B, Aᶜ, and Bᶜ, and use the information above to calculate the probability of each. i. Consolidated wins both jobs. P(A ∩ B) = 0.1 ii. Consolidated wins the first job but not the second. P(A ∩ Bᶜ) = 0.5 iii. Either Consolidated does not win the first job or wins the second. P(Aᶜ ∪ B) = 0.1 + 0.2 + 0.2 = 0.5 iv. Consolidated does not win either job. P(Aᶜ ∩ Bᶜ) = 0.2