Probability Questions & Answers

3 Numeric 20 points In a standard deck, there are 52 cards. Twelve cards are face cards ( \( F \) ) and 40 cards are not face cards ( N ). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities. Find \( \mathrm{P}(\mathrm{FN} \) OR NF). give your answer correct to 4 decimal places.

A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. The probability that a student selected at random believed the true headline was \( 90 \% \) and the probability that the student believed the false headline was \( 82 \% \). She found that \( 75 \% \) of the students believed both headlines. In this sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive? Choose 1 answer: (A) Yes B No Find the probability that a randomly selected person from this sample believed the true headline OR believed the false headline. P (believed true OR believed false) =

Denis examined the records of the clients at his gym, and he found these statistics: \( P \) (joined in January) \( =0.12 \) \( P \) (member for over 6 months \( )=0.5 \) \( P( \) over 6 months and January \( )=0.024 \) Find the probability that a client remained a member for more than 6 months, given that the client joined in January. \( P \) (over 6 months \( \mid \) January \( )= \)

Please write your name clearly inside this box: Remember to show your work! Without sufficient work, marks will not be given. 1. I plan to have a treat and watch a movie. I can pick an animated movie, a comedy, or an adventure movie. For dessert, I can choose an ice cream cone, a milkshake, pie, cake, or a candy bar. How many possibilities are there for the sequence of events? 2. A Mount SIS ID consists of six digits i.e. 143253 . (a) How many different codes are there? (b) How many different functions from \( B \) to \( A \) are there? (a) How many different functions from \( A \) to \( B \) are there? (b) How many codes contain only odd digits? (c) How many codes contain at least 1 evan 4 sit? (and \( B \) be two sets with \( |A|=5 \) and \( |B|=6 \). (a) (a)

A bissed coin has been tossed 123 times with the result of 86 Heads. Calculate the relative frequency of the coin landing Tails.

2) De la ciudad A a la ciudad B, se puede ir mediante 2 buses o 3 trenes. De la ciudad B a la ciudad C se puede ir mediante 2 barcos, 2 trenes o 3 aviones. ¿De cuántas formas se puede ir de la ciudad A a la ciudad C, pasando por B?

8) En un club deportivo se quieren cubrir tres puestos, el de presidente, secretario y tesorero, para ello hay 10 candidatos. Si el puesto de presidente ya ha sido ocupado, ¿de cuántas formas se pueden cubrir los otros dos puestos?

8) En un club deportivo se quieren cubrir tres puestos, el de presidente, secretario y tesorero, para ello hay 10 candidatos. Si el puesto de presidente ya ha sido ocupado, ¿de cuántas formas se pueden cubrir los otros dos puestos?

9) En un campeonato de fútbol participan 8 equipos locales. ¿De cuántas maneras distintas pueden ser ocupados los tres primeros lugares?

Estas bolitas numeradas tienen igual peso y tamafo, tres son grises y las demás son blancas. Se echan las bolitas a una caja y se extrae una al azar. ¿Cuál es la probabilidad de que la bolita extraida sea gris o tenga un número par? (A) \( \frac{2}{3} \) (B) \( \frac{1}{4} \) (C) \( \frac{5}{8} \) (D) \( \frac{7}{8} \)