The questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:
1. One equal sign per line,
2. Equal signs in each question lined up vertically with each other,
3. No self-developed short form notations,
4. One step or idea per line,
5. Show complete solution to the given problem.
1. A six-member working group to plan a student lounge is to be selected from five teachers and nine students. If the working group is randomly selected, what is the probability of the committee including at least two teachers.
2. Cha'tima has five white and six grey huskies in her kennel. If a wilderness expedition chooses a team of six sled dogs from Cha'tima's kennel, what is the probability that the team will consist of:
a. all white huskies?
b. all grey huskies?
c. three of each colour?
3. A survey at a school asked students if they were ill with a cold or the flu during last months.
The results were as follows. None of the students had both a cold and the flu.
Cold Flu Healthy
Females 32 18 47
Males 25 19 38
Use these results to estimate the probability that:
a. a randomly selected student had a cold last month.
b. a randomly selected females students was healthy last month.
c. a randomly selected student who had the flu last month is male.
d. a randomly selected student had either a cold or the flu last month.
4. To get out of jail free in the board game Monopoly, you have to roll doubles with a pair of dice. Determine the odds in favor of getting out of jail on your first or second roll.
5. If a survey on teenage reads of popular magazines shows that 38% subscribe to Teen Life and 47% subscribe to Cool Teen and 35% subscribe to neither magazine, what is the probability that a randomly selected teenager,
a. subscribes to both magazines?
b. subscribes to either one magazine or both?
c. subscribes to only one of the two magazines?
Use a Venn diagram to support your solution.
The solution provides step by step method for the calculation of probability based on frequency approach . Formula for the calculation and Interpretations of the results are also included.