Probability preguntas y respuestas

QUESTION 8 8.1 At a certain school there are 64 boys in Grade 10 . Their sport preferences are indicated below: \begin{tabular}{ll} - 24 boys play soccer \\ - 28 boys play rugby \\ 10 boys play both soccer and rugby \\ 22 boys do not play soccer or rugby \\ 8.1 .1 & Represent the information above in a Venn diagram. \\ 8.1 .2 & \( \begin{array}{l}\text { Calculate the probability that a Grade } 10 \text { boy at the school, selected at } \\ \text { random, plays: }\end{array} \) \\ (a) Soccer and rugby & (b) Soccer or rugby \\ 8.1 .3 & \( \begin{array}{l}\text { Are the events a Grade } 10 \text { boy plays soccer at the school and a Grade } 10 \\ \text { boy plays rugby at the school, mutually exclusive? Justify your answer. }\end{array} \) \\ \hline\end{tabular}

A "handoff" is a term used in wireless communications to describe the process of a cell phone moving from the coverage area of one base station to that of another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. A certain engineering magazine published a study of cell phone handoff behavior. During a sample driving trip that involved crossing from one base station to another, the different color codes accessed by the cell phone were monitored and recorded. The table below shows the number of times each color code was accessed for two identical driving trips, each using a different cell phone model. Suppose you randomly select one point during the combined driving trips. Complete parts a through c. a. What is the probability that the cell phone was using color code c? The probability is (Round to three decimal places as needed.)

A "handoff" is a term used in wireless communications to describe the process of a cell phone moving from the coverage area of one base station to that of another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. A certain engineering magazine published a study of cell phone handoff behavior. During a sample driving trip that involved crossing from one base station to another, the different color codes accessed by the cell phone were monitored and recorded. The table below shows the number of times each color code was accessed for two identical driving trips, each using a different cell phone model. Suppose you randomly select one point during the combined driving trips. Complete parts a through c. a. What is the probability that the cell phone was using color code c? The probability is (Round to three decimal places as needed.)

A "handoff" is a term used in wireless communications to describe the process of a cell phone moving from the coverage area of one base station to that of another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. A certain engineering magazine published a study of cell phone handoff behavior. During a sample driving trip that involved crossing from one base station to another, the different color codes accessed by the cell phone were monitored and recorded. The table below shows the number of times each color code was accessed for two identical driving trips, each using a different cell phone model. Suppose you randomly select one point during the combined driving trips. Complete parts a through c. a. What is the probability that the cell phone was using color code c? The probability is \( \square \). (Round to three decimal places as needed.)

In a sample of 1995 adults from a certain region, 1505 reported that they currently receive cable or satellite TV service at home, 198 revealed that they have never subscribed to a cable/satellite TV service at home, and 292 admitted that they are "cord cutters," i.e., they canceled the cable/satellite TV service. One of the surveyed adults is randomly selected and his or her cable TV subscription status is determined. Complete parts a through d. c. What is the probability that the adult has never subscribed to cable/satellite TV service? The probability is \( \square \). (Round to three decimal places as needed.) d. What is the probability that the adult has currently or previously subscribed to cable/satellite TV service? The probability is \( \square \). (Type an integer or a decimal.)

An experiment results in one of the sample points \( E_{1}, E_{2}, E_{3}, E_{4} \), or \( E_{5} \). Complete parts a through \( c \). a. Find \( P\left(E_{3}\right) \) if \( P\left(E_{1}\right)=0.2, P\left(E_{2}\right)=0.2, P\left(E_{4}\right)=0.2 \), and \( P\left(E_{5}\right)=0.2 \). \( P\left(E_{3}\right)=\square \) (Type an exact answer in simplified form.) b. Find \( P\left(E_{3}\right) \) if \( P\left(E_{1}\right)=P\left(E_{3}\right), P\left(E_{2}\right)=0.2, P\left(E_{4}\right)=0.2 \), and \( P\left(E_{5}\right)=0.1 \). \( P\left(E_{3}\right)=\square( \) Type an exact answer in simplified form.) c. Find \( P\left(E_{3}\right) \) if \( P\left(E_{1}\right)=P\left(E_{2}\right)=P\left(E_{4}\right)=P\left(E_{5}\right)=0.2 \).

A construction company employs three sales engineers. Engineers 1,2 , and 3 estimate the costs of \( 15 \%, 25 \% \), and \( 60 \% \), respectively, of all jobs bid on by the company. For \( i=1,2,3 \), define \( E_{1} \) to be the event that a job is estimated by engineer \( i \). The following probabilities describe the rates at which the engineers make serious errors in estimating costs: \( P\left(\right. \) error \( \left.\mid E_{1}\right)=0.04, P\left(e r r o r \mid E_{2}\right)=0.03 \), and \( P\left(\right. \) error \( \left.\mid E_{3}\right)=0.02 \). Complete parts a through \( d \). c. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 3 ? \( P\left(E_{3} \mid e r r o r\right)=\square \) (Round to the nearest thousandth as needed.) d. Based on the probabilities, given in parts a-c which engineer is most likely responsible for making the serious error?

A construction company employs three sales engineers. Engineers 1,2 , and 3 estimate the costs of \( 15 \%, 25 \% \), and \( 60 \% \), respectively, of all jobs bid on by the company. For \( i=1,2,3 \), define \( E_{i} \) to be the event that a job is estimated by engineer \( i \). The following probabilities describe the rates at which the engineers make serious errors in estimating costs: \( P\left(\right. \) error \( \left.\mid E_{1}\right)=0.04, P\left(e r r o r \mid E_{2}\right)=0.03 \), and \( P\left(\right. \) error \( \left.\mid E_{3}\right)=0.02 \). Complete parts a through \( d \). a. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1 ? \( P\left(E_{1} \mid\right. \) error) \( =\square \) (Round to the nearest thousandth as needed.) b. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 2 ?

QUESTION 7 7.1 An Ice-Cream fridge has 13 Chocolate flavoured ice-creams, 12 Cappuccino flavoured ice-creams and \( x \) number of Orange flavoured ice-creams. 7.1.1 If there is a \( 50 \% \) of choosing an orange flavoured ice-cream, how many orange ice -creams are in the fridge? 7.1.2 Determine the probability of choosing two of the same flavoured ice-cream one after each other if the ice cream is not replaced. Give your answer rounded to 2 decimal places.

For two events, \( A \) and \( B, P(A)=0.5, P(B)=0.4 \), and \( P(A \mid B)=0.75 \). a. Find \( P(A \cap B) \). b. Find \( P(B \mid A) \). a. \( P(A \cap B)=\square \) (Simplify your answer.) b. \( P(B \mid A)=\square \) (Simplify your answer.)