How to solve

Chapter $2$

$2\mathrm{.}6$ There are four targets and a shooter. The shooter selects one of the targets randomly. Shooter may select a target again even if it was shot and hit. before. The probability of hit is $0\mathrm{.}6.$ The shooter shoots six times.

a$.$ What is the probability that Target $x$ is shot at least one time?

b$.$ What is the probability that Target $x$ is hit at least one time?

c$.$ What is the probability that the shooter hits a target all six times?

d$.$ What is the probability that the shooter misses everytime?

e$.$ What is the probability that the shooter hits two times?

f$.$ What is the probability that the shooter hits a target first time at his third trial?

g$.$ What is the probability that Target $x$ is never shot?

h$.$ What is the probability that the shooter selects Target $x$ all six times?

i$.$ What is the probability that Target $x$ is hit six times?

$2\mathrm{.}7$ In an exam of $10$ multiple choice questions, the students must answer $5$ or more questions correctly to pass the exam. Each question has $4$ multiple choices. If a student answers all the questions randomly, what is the probability that the student passes the exam?

$2\mathrm{.}8$ There are $13$ students in a course. They will visit Site A and Site B$.$ They are selected for the sites randomly.

a$.$ How many different options are there to pick $6$ for Site A and $7$ for Site B$?$

b$.$ How many different options are there to pick $6$ for Site A and $6$ for Site B$?$ The student that cannot join the site visits is randomly picked.

c$.$ One of the students cannot join the site visits and the student who cannot join is known. How many different options are there to pick $6$ for Site A and $6$ for Site B$?$

$2\mathrm{.}9$ There are $13$ students in a course. $6$ and $7$ students will visit Site A and Site B respectively. They are selected for the sites randomly. What is the probability that a student is selected to visit Site A$?$

$2\mathrm{.}10$ There are $13$ students in a course. They will visit three sites. $3,6$ and $4$ students will visit Sites A$,$ B and C$.$ They are selected for the sites randomly. How many different options are there to assign students to these three sites?