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76 Questions around this concept.
Let $\mathrm{S}=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number n from the set S such that $\operatorname{HCF}(\mathrm{n}, 2022)=1$, is :
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :
If two different numbers are taken from the set {0, 1, 2, 3, ......, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :
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Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it. The number of females qualifying for the exam is twice the number of males qualifying for it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is:
If three coins are tossed simultaneously the probability of getting at least one head is.
What is the chance that a leap year, selected at random, will contain 53 Saturdays?
A box contains 4 while balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is
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Basic Probability Practise Session 1
Q1. Let a natural number 'n' is selected, then find the probability that 4th power of n' ends in digit 6 is ?
Q2. There are 10 red and 15 green balls. Find the probability, if:
(i) if one ball is drawn and it is red.
(ii) if two balls are drawn in succession then one is, red and other is green
Q3. If a letter is selected from the word OPPOSITION, find the probability, that:
(i) a letter selected is a vowel?
(ii) It the letters are rearranged in such a way that "no two O can occur together"?
Q4. There 6 boys and 6 girls. What is the probability that boys and girls sit alternately?
Basic Probability Practise Session 2
Q1. There are N letters and N envelops. Find the probability such that all the letters are not kept in their right envelope?
Q2. In a well-shuffled deck of cards, one card is picked. What is the probability that this card is neither a heart nor a king?
Q3. A die is rolled 4 times. Out of 4 faces obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5?
Q4. Two dices are rolled simultaneously. Find the probability such that the sum of the digits on faces is greater than 7?
Q5. Three dices are rolled simultaneously, Find the probability such that the sum of faces on the digits is greater than 13.
Basic Probability Practise Session 3
Q1. There are 21 tickets in a box numbered 1 to 21. If three tickets are picked randomly. Find the probability that the tickets picked are in AP?
Q2. There are 3 oranges and 4 apples randomly placed in a line. Find the probability of the extreme fruits being both oranges?
Q3. What is the probability that out of the group of N people, at least two of them will have the same birthday? (Given that N<365 and the year is non-leap).
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