Probability

The post is about the Online Probability MCQs Questions. There are 20 multiple-choice questions covering topics related to random experiments, random variables, probability, classical and empirical probability, rules of probability (addition and multiplication rule), conditional probability, events, types of events, and sample space. Let us start with the Probability MCQs Questions Quiz.

Online Probability MCQs Questions with Answers

• What is the probability of getting two heads when two coins are tossed/flipped?
• The probability of getting a double by rolling TWO six-sided dice (with sides labeled as 1, 2, 3, 4, 5, 6) is:
• You roll a dice five times. The outcomes are: 6, 6, 6, 6, 6. Then you repeat this and you find: 1, 4, 3, 5, 2. Which of the following outcomes is most likely?
• You ask a couple of people at the beach what they think about the seagulls. You propose to them the statement: Seagulls are annoying. Their responses are as follows: 20% Strongly Agree 13% Agree 12% Neutral 50% Disagree 5% Strongly Disagree What is the chance of a random person responding with ‘agree’ given that he/she is not neutral?
• You ask some students which subject they prefer: statistics or English. There are a lot of people who love statistics ($B$) and a lot of people who love English ($C$). However, some people cannot make a decision and tell you that they like both subjects ($D$). Getting some insights about results, you realized that all the female students had a positive opinion about statistics ($A$). Which of these events ($A$, $B$, $C$, $D$) are disjoint?
• Suppose, you collected four shells from a beach. It is known that there are only three types of shells on this beach, and these shells occur in equal amounts. How many different events are possible?
• Twenty people take a statistics exam. Usman scored five out of ten and Ali scored eight out of ten. Every score (1 to 10) is equally likely. What is the chance of a random person out of the people who took the exam scoring higher than Usman, but lower than Ali?
• How can we define probability or chance? MCQs General Knowledge
• Suppose that you are rushing out to get to your appointment in 30 minutes. From experience, you know that most of the time you travel this distance in 30 minutes. However, half of the time there is heavy traffic. In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time. You get out on the street and see that there is heavy traffic. What is the chance you will get to your appointment on time?
• A pot has 100 balls. 20 of them are red, 50 are blue and 30 are green. You draw 5 balls from the pot without replacement. What is the probability of drawing five blue balls?
• On a single train journey, there is a probability of 0.4 that your ticket will be checked. You make a return-journey, what is the probability that your ticket will be checked only once? R Programming Language
• A pair of dice is rolled 20 times and record how often you get a total of 5 or 10. What is your best guess for the relative frequency that this event (a total of 5 or 10) occurs without seeing the actual data?
• If $P(A \,\, and\,\, B)= P(A|B) \cdot P(B)$ then both events are
• If the probability that event $A$ occurs is 0.51 and the probability that event $B$ occurs is 0.64. Both events $A$ and $B$ are statistically independent, then
• If the probability that event $A$ occurs is 0.51 and the probability that event $B$ occurs is 0.64. The probability that both $A$ and $B$ occur is 0.23, then
• If three boys are randomly selected, and the probability that they will all have birthdays in June is
• Three dice are rolled. What is the probability of getting three 4s?
• If $P(A\cap B)=\phi$ then $P(A\cup B)=$
• Empirical probability is based on
• Which of the two events are mutually exclusive?

R Programming Language, MCQs General Knowledge

This post is about some solved probability questions. These questions make use of (i) the Addition Law of Probabilities, and (ii) the Multiplication Law of Probabilities.

Solved Probability Questions

Question 1: Box A contains 5 Green and 7 Red balls. Box B contains 3 Green, 3 Red, and 6 Yellow balls. A box is selected at random, and a ball is drawn at random from it. What is the probability that the bill drawn is green?

Solution:

Box A

Total Balls: 5 + 7 = 12
Prob(Green) = $\frac{3}{12}$

Box B

Total Balls: 3 + 3 + 6 = 12
P(Green) = $\frac{3}{12} = \frac{1}{4}$

$$P(A+B) = P(A) + P(B) = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}$$

Question 2: A pair of fair dice is thrown twice. What is the probability of getting a total of 5 or 11?

Solution:

\begin{align*}
P(X = 11 \,\, or X = 5) &= P(X=11) + P(X=15) – P(X=11\,\,and\,\, X=5)\\
P(X=11) &= \frac{2}{36}\\
P(X=5) &= \frac{4}{36}=\frac{1}{9}\\
P(X=11\,\, and X=5) &= 0
\end{align*}

Therefore,

\begin{align*}
P(X=11\,\, or X=5) &= P(X=11) + P(X=5) \\
&=\frac{2}{36} + \frac{1}{9} = \frac{1}{6}
\end{align*}

Note that $P(X=11\,\, and X=5) = 0$, because the sum of two dice cannot be at the same time 5 and 11.

Question 3: A marble is drawn at random from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles. What is the probability that it is (i) orange or red (ii) not red or blue (iii) not blue, (iv) white, (v) red, white, or blue.

Solution:

Total number of balls = 10 + 30 + 20 + 15 = 75
Number of Orange balls = 15
Number of Blue balls = 20
Number of White balls = 30
Number of Red balls = 10

1. P(a marble drawn is red or orange) = P(Red marble) + P(Orange marble)
   $$=\frac{10}{75} + \frac{15}{75} = \frac{1}{3}$$
2. P(a marble drawn is not red or blue) = P(not Red) + P(Blue) – P(Blue and not Red)
   $$=\frac{65}{75} + \frac{20}{75} – \frac{20}{75} = \frac{65}{75}$$
3. P(a ball drawn is not Blue) = $1 – P(Blue) = 1 – \frac{20}{75} = 0.733$
4. P(a ball drawn is white) = $\frac{30}{75}$
5. P(a ball drawn is Red, White, or Blue) = P(Red) + P(White) + P(Blue)
   $$=\frac{10}{75} + \frac{30}{75} + \frac{20}{75} = \frac{60}{75}$$

Question 4: If two dice are thrown what are the various total number of dots that may turn up? What are the probabilities of each of them? What is the probability that the number of dots will total at least four?

Solution:

When two dice are thrown together, the minimum total number of dots is 2 (1, 1), and the maximum dots possible are 12 (6, 6). Therefore

• Probability of 2 dots (1, 1) = $\frac{1}{36}$
• Probability of 3 dots {(2, 1), (1, 2)} = $\frac{2}{36} = \frac{1}{18}$
• Probability of 4 dots {(2,2) (3,1) (1,3)} = $\frac{3}{36} = \frac{1}{12}$
• Probability of 5 dots {(4,1) (1,4) (2,3) (3,2)} = $\frac{4}{36} = \frac{1}{9}$
• {Probability of 6 dots {(3,3) (4,2) (2,4) (5,1) (5,1)} = $\frac{5}{36}$
• Probability of 7 dots {(4,3) (3,4) (5,2) (2,5) (6,1) (1,6)} = $\frac{6}{36} = \frac{1}{6}$
• Probability of 8 dots {(6,2) (2,6) (5,3) (3,5) (4,4)} = $\frac{5}{36}$
• Probability of 9 {(5,4) (4,5) (6,3) (3,6)} dots = $\frac{4}{36} = \frac{1}{9}$
• Probability of 10 dots {(5,5) (6,4) (4,6)} = $\frac{3}{36} = \frac{1}{2}$
• Probability of 11 dots {(5,6) (6,5)} = \frac{2}{36} = \frac{1}{18}$
• Probability of 12 dots {(6,6)} = $\frac{1}{36}$
• Probability that the number of dots will total at least 4 = $\frac{33}{36}$

Question 5: A one card is selected at random from a deck of 52 playing cards. What is the probability that the card is a club or a face card or both?

Solution:

\begin{align*}
P(club\,\, or\,\, face\,\, or\,\, both) &= P(club) + P(face) – P(club\,\, and\,\, face)\\
&=\frac{13}{52} + \frac{12}{52} – \frac{3}{52} = \frac{11}{26}
\end{align*}

Question 6: A class contains 10 men and 20 women of which half men and half women have brown eyes. What is the probability that a person chosen at random is a man or has brown eyes?

Solution:

Let $A$ be the event that it is a man (10 out of 30)
Let $B$ be the event that the person has brown eyes (5 men and 10 women: 15 out of 30)

$P(A\cap B)$ is a man AND has brown eyes $\frac{5}{30}$

\begin{align*}
P(A \cup B) &= P(A) + P(B) – P(A \cap B)\\
&= \frac{10}{30} + \frac{15}{30} – \frac{5}{30} = \frac{2}{3}
\end{align*}

Question 7: A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rested. If one item is chosen at random, what is the probability that it is rusted or is a bolt?

Solution:

Number of Bolts = 50
NUmber of Nuts = 150
Total number of Items = 50 + 150 = 200

Item chosen is rusted: $P(A) = \frac{100}{200} = \frac{1}{2}$
Item chosen is bolt: $P(B) = \frac{50}{200} = \frac{1}{4}$
Ite is Rusted and Bolt = $P(A\cap B) = P(A) \cdot P(B) = \frac{1}{2}\cdot \frac{1}{4} = \frac{1}{8}$

\begin{align*}
P(A \cup B) &= P(A) + P(B) – P(A\cap B) \\
&= \frac{1}{2} + \frac{1}{4} – \frac{1}{8} = \frac{5}{8}
\end{align*}

Learn R Programming, Computer MCQs Online Test

The post is about Probability Quiz Online. There are 20 multiple-choice questions covering topics related to events and types of events, laws of probability, dependent and independent events, sample space, and probabilities related to coins, dice, and standard deck of cards. Let us start with Probability Quiz Online.

Please go to MCQs Probability Quiz Online 11 to view the test

MCQs Probability Quiz Online

• The probability of the occurrence of the event ‘$A$’ is $P(A)=$
• When the occurrence of an event does affect the probability of the occurrence of another event it is called
• The probability of a sample space is equal to
• If three coins are tossed, the all possible cases are
• If a fair dice is rolled, the sample space is
• A fair dice is rolled twice, and the probability of getting a sum 8 is
• If $A$ and $B$ are mutually exclusive events then $P(A \cup B)=$
• If $A$ and $B$ are not mutually exclusive events then $P(A\cup B)=$
• If $A$ and $B$ are independent events then $P(A\cap B)=$
• If $A$ and $B$ are dependent events then $P(A \cap B) =$
• The probability of drawing a picture card from a pack of 52 cards is
• The probability of drawing a diamond card from a pack of 52 cards is
• The probability of drawing a ball at random from the box is
• For two mutually exclusive events $A$ and $B$, $P(A) = 0.3$ and $P(B)=0.5$ then $P(A \cup B)$ is
• If $P(B|A)=0.30$ and $P(A \cap B)=0.12$ then $P(A)$ is
• The probability of an event $A$ lies between
• If $P(A \cap B) = \phi$ then $P(A \cup B)=$ ————-.
• When an event is certain to occur, its probability is
• Baye’s Theorem
• The term “Sample Space” is used for

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