Probability Questions & Answers

b. A dice was rolling and it sample is \( S=\{1,2,3,4,5,6\} \) \[ A=\{2,4,5\} \quad B=\{1,3,4,5,6\} \] i. \( P(A \cap B) \) ii. \( P(A \cup B) \) iii. \( P(A \) complement \( ) \)

10N 7 \( A \) bag contains 3 green balls and 5 red balls. The balls are placed in a bag and or chosen at random. Determine the probability that the ball selected is red. Two events \( A \) and \( B \) are complementary and also \( P( \) not \( A)=0.25 \) 7.2 .1 7.2 .2 Write down the value of \( P(A) \).

c. Find the probability the firefighter is a female. \( \mathrm{P}( \) female \( )=\square \) (Round to three decimal places as needed.) d. Find the probability the glove fits well. P (well) \( =\square \) (Round to three decimal places as needed.) e. Find the probability the firefighter is a male and has a poorly-fitting glove. P (male and poorly-fitting) \( =\square \) (Round to three decimal places as needed.)

b. Assign reasonable probabilities to the sample points. List the probabilities in the same order as the sample points found in part a, rounding to three decimal places. Choose the correct answer below. A: \( 0.698,0.232 \) B. \( 0.25,0.25,0.25,0.25 \) C. \( 0.698,0.232,0.031,0.039 \) D. \( 0.302,0.768,0.969,0.961 \) E. \( 0.930,0.070,0.729,0.271 \)

a. \( A \) and \( B \) are event with \( P(A)=0.2, P(B)=0.16 \) and \( P(A \cap B)=0.04 \) i. Calculate \( P(A \cup B) \) i. Explain whatever \( A \) and \( B \) are mutually exclusive events

b. Use the information in the pie chart to estimate the probability that an American believes the Americar Dream is either out of reach or pessimistic about reaching it. The probability is

a. Use the information in the pie chart to estimate the probability that an American believes he or she has achieved the American Dream. The probability is \( \square \). (Type an integer or a decimal. Do not round.)

In a certain region, the competition for social networking is between Network A and Network B. According to a survey, \( 8 \% \) of the region's citizens visit Network A, \( 6 \% \) visit Network B, and \( 3 \% \) visit both Network A and Network B. Complete parts a through c. b. Find the probability that a citizen from the region visits either Network A or Network B. The probability is \( \square \). (Simplify your answer.) c. Use your answer to part b to find the probability that a citizen from the region does not visit either social networking site. The probability is \( \square \).

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.)

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}