In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays is:
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$\frac{1}{7}$
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$\frac{2}{7}$
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$\frac{3}{7}$
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none os these.
Question types
Probability question types
52 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
52
Questions
7
Question groups
5
Question types
01
M.C.Q (1 Marks)
12 Q→02True False[1 Marks ]
7 Q→03Fill In The Blanks[1 Marks ]
5 Q→041 Marks Question
6 Q→052 Marks Questions
2 Q→063 Marks Question
10 Q→075 Marks Questions
10 Q→Sample Questions
Probability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is:
-
$\frac{1}{432}$
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$\frac{12}{431}$
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$\frac{1}{132}$
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none of these.
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then $\text{P}(\bar{\text{A}})+\text{P}(\bar{\text{B}})$ is:
- 0.4
- 0.8
- 1.2
- 1.6
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is:
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$\frac{1}{3}$
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$\frac{4}{11}$
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$\frac{2}{11}$
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$\frac{3}{11}$
While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours:
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$\frac{29}{52}$
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$\frac{1}{2}$
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$\frac{26}{51}$
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$\frac{27}{51}$
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
The probability that a person visiting a zoo will see the giraffee is 0.72, the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.
The sum of probabilities of two students getting distinction in their final examinations is 1.2
The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is .3 and the probability of occurrence of both is 0.4
The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is __________.
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is ____________.
View full solution →If e1, e2, e3, e4 are the four elementary outcomes in a sample space and P(e1) = 0.1, P(e2) = 0.5, P (e3) = 0.1, then the probability of e4 is ___________.
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is __________.
Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then $\bar{\text{E}}$is __________.
View full solution →If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}'\cap\text{B}')$
View full solution →$\text{P}(\text{A}'\cap\text{B}')$
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cap\text{B})$
View full solution →$\text{P}(\text{A}\cap\text{B})$
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
P(A')
P(A')
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cap\text{B}')$
View full solution →$\text{P}(\text{A}\cap\text{B}')$
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cup\text{B})$
View full solution →$\text{P}(\text{A}\cup\text{B})$
An experiment consists of rolling a die until a 2 appears:
How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die?
[Hint: First (k - 1) rolls have 5 outcomes each and kth rolls should result in 1 outcomes]
How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die?
[Hint: First (k - 1) rolls have 5 outcomes each and kth rolls should result in 1 outcomes]
A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that:
- All the three balls are white.
- All the three balls are red.
- One ball is red and two balls are white.
If the letters of the word ASSASSINATION are arranged at random. Find the Probability that:
Two I’s and two N’s come together.
Two I’s and two N’s come together.
If the letters of the word ASSASSINATION are arranged at random. Find the Probability that:
All A’s are not coming together.
All A’s are not coming together.
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
If the letters of the word ASSASSINATION are arranged at random. Find the Probability that:
Four S’s come consecutively in the word.
Four S’s come consecutively in the word.
Determine the probability p, for each of the following events.
- An odd number appears in a single toss of a fair die.
- At least one head appears in two tosses of a fair coin.
- A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
- The sum of 6 appears in a single toss of a pair of fair dice.
Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that:
- C will be selected?
- A will not be selected?
One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John’s promotion is same as that of Gurpreet, Rita’s chances of promotion are twice as likely as Johns. Aslam’s chances are four times that of John:
P(Rita promoted)
P(Aslam promoted)
P(Gurpreet promoted)
- Determine P(John promoted)
P(Rita promoted)
P(Aslam promoted)
P(Gurpreet promoted)
- If A = {John promoted or Gurpreet promoted}, find P(A).
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections $($for instance, $\text{P}(\text{A}\cap\text{B})=.07)$ Determine:
View full solution → - $\text{P(A)}$
- $\text{P}(\text{B}\cap\bar{\text{C}})$
- $\text{P(A}\cup\text{B})$
- $\text{P(A}\cap\bar{\text{B}})$
- $\text{P(B}\cap\text{C})$
- Probability of exactly one of the three occurs.
Match the following:
View full solution →| a. | If E1 and E2 are the two mutually exclusive events | i. | $\text{E}_1\cap\text{E}_2=\text{E}_1$ |
| b. | If E1 and E2 are the mutually exclusive and exhaustive events | ii. | $(\text{E}_1-\text{E}_2)\cup(\text{E}_1\cap\text{E}_2)=\text{E}_1$ |
| c. | If E1 and E2 have common outcomes, then | iii. | $\text{E}_1\cap\text{E}_2=\phi,\text{ E}_1\cup\text{E}_2=\text{S}$ |
| d. | If E1 and E2 are two events such that $\text{E}_1\subset\text{E}_2$ | iv. | $\text{E}_1\cap\text{E}_2=\phi$ |
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