University:
Minnesota State University Moorhead
Course:
MATH-335 | Intermediate Probability and Statistics I
Academic year:

2020
Views:

138

Pages:

2
Author:

Efrain Villa

Supplemental worksheet 7.3 Conditional Probability 1. A survey of 500 college students regarding their preference about school system: semester or quarter. We can classify them by gender: Male or female; by vote; prefer Quarter or not quarter. You are given n(M) = 300 n(Q) = 280, n(M ∩ Q) = 160. a. Make a two-way table use the information provided. Compare this with a Venn Diagram. NO Prefer/Gender Q Q^c Total Male M 160 140 300 Female M^c 120 80 200 Total 280 220 500 b. Estimate the following profanities: i. P (M) = 160/500 = 3/5 = 0.6  60% ii. P (Q) = 280/500 = 14/25 = 0.56  56% iii. P (M ∩ Q) = 160/500 = 8/25 = 0.32  32% c. Estimate the following conditional probabilities: i. P (M|Q) = 160/280 = 4/7 = 0.57  57% ii. P (Q|M) = 160/300 = 8/15 = 0.53  53% iii. P (M|M) = 0 2. One card is randomly dealt from a standard deck, let event D=diamond, F = face card, calculate the following conditional probabilities; a. P (D|F) = 3/12 = ¼ = 0.25  25% b. P (F|D) = 3/13 = 0.23  23% D D^c Total F 3 9 12 F^c 10 30 40 13 c. d. e. f. 39 52 P (F|F) = 0 P (D ∩ F) = 3/52 = 0.058  5.8 % P (D ∪ F) = 13+12-3 = 22/52 = 11/26 = 0.42  42.3 % Are events D and F independent to each other? P (D) = 13/52 = ¼ P (D|F) = ¼ D and F are independent variables