Statistics and Probability Answers

Theorems of addition of probability and theorems of multiplication of probabilities are used for solving
1. There are 30 students in the group. The marks for the control test were the
following: 8 students received “excellent” marks, 12 students - “good” marks, 8
students – “satisfactory”. What is the probability that 3 students invited for answer have “good” marks?

Total probability formula and Bernoulli formula is used for solving
1. There exists 2 student’s group with 30 people in each of them. There are 5 students in the first
group who have the mark “5” on anatomy, 15 students – “good” marks. From the second group
only 3 students have “5” and 10 students – “good”. One student will be chosen from these 2
groups for taking part in the conference. Find out the probability that he will have the mark “5” on
anatomy.

Theorems of addition of probability and theorems of multiplication of probabilities are used for solving
1. What is the probability of drawing either a king or a queen in a single drawing from a deck of 52 playing cards?
2. There are 3 children in family. The birth o a girl and a boy is considered to be
equally possible. Find out the probability of the fact that all children in the family
are boys.

The probability is 0.70 that a rare tropical disease will be diagnosed correctly. If it is diagnosed correctly, the probability is 0.90 that the patient will be cured; if it is not diagnosed correctly, the probability is 0.40 that the patient will be cured.
i. Draw a tree diagram to represent all the probabilities.

qualitive data can be graphically represented by using a

A high correlation between two explanatory variables such that the two variables contribute redundant information to the model is known as

One bag contains 5 white balls and 4 black balls and the second bag contains 3 white balls and 2 black balls.one ball is drawn from the first bag and placed unseen in the second bag. What is the probability that the ball now drawn from the second bag is black?

4. RATSA is planning to enforce speed limits along Great North road by
using speed cameras at 4 different locations, L1, L2, L3 and L4. The
speed camera at L1 is operated 50% of the time, the speed camera at
L2 is operated 30% of the time, the speed camera at L3 is operated 20%
of the time and the speed camera at L4 is operated 40% of the time.
A person who is speeding from for work has probabilities 0.2, 0.1, 0.5
and 0.2 respectively, of passing through these locations.
(i) What is the probability that the person will receive a speed ticket?
(ii) If the person received the speed ticket, what is the probability
that it was at L3 where he violated speed limit rules?