Probability Questions & Answers

2. (a) A vet can detect a particular lilness in a dog with probability 0.92 . Once the illness is detected, the Iliness can only be treated through one or two operations. The first operation cures dogs with probability 0.85 . If the first operation is not successful, the dog gets a second operation. This second operation has 0.65 probability of success. For a dog visiting the vet with this iliness, work out the probability that: (I) the dog is cured after one operation.

\begin{tabular}{l} March Madness Movies served 23 lemonades out of a total of 111 \\ fountain drinks last weekend. \\ Based on this data, what is a reasonable estimate of the probability that \\ the next fountain drink ordered is a lemonade? \\ Choose the best answer. \\ Choose 1 answer: \\ \hline (A) \( \frac{23}{111} \) \\ (B) \( \frac{23}{88} \) \\ (C) \( \frac{111}{111} \) \\ (D) \( \frac{88}{111} \)\end{tabular}

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?