hard probability questions

Event $A_1$. When it doesn't rain, he incorrectly forecasts rain $10%$ of the time. 25, 4x4 squares Event $A_2$. The dice is rolled and Bob writes down a number in his notebook, if it has not already been written down. Edit: For an alternative solution, check comment from Bhavya Shah. Two squares are chosen at random on a chessboard. of Ways = ${^{32}C_4} × {^{32}C_0}$. The higher the probability of an event, the more likely it is to occur, i. E. Tossing a coin gives a 50% chance of getting heads or tails. 8. ], \(P(A_2)=\dfrac{360}{365}=0.9863013\) [It does not rain 360 days out of the year. Some problems are easy, some are very hard, but each is interesting in some way. Almost all problems I have heard from other people or found elsewhere. Frequently asked simple and hard probability problems or questions with solutions on cards, dice, bags and balls with replacement covered for all competitive exams,bank,interviews and entrance tests. Now if we assume that 2 squares can have a side common only if they are of the same dimensions: What is the probability that it will rain on the day of Marie's wedding? Hedge Fund Interview Sample Pitches - Long/Short. What is the probability that the person, chosen as the leader is a boy? The application of probability can be seen in Maths as well as in day to day life. Sample Probability questions with solutions. of Ways = ${^{32}C_1} × {^{32}C_3}$, White = 2, Black = 2, No. The Corbettmaths Practice Questions on Probability. of Ways = ${^{32}C_3} × {^{32}C_1}$, White = 4, Black = 0, No. Would you spare a moment and help us improve it. of Ways = ${^{32}C_0} × {^{32}C_4}$, White = 1, Black = 3, No. if we consider that total squares are more than 64). When it actually rains, the weatherman correctly forecasts rain $90%$ of the time. of Ways = ${^{32}C_2} × {^{32}C_2}$, White = 3, Black = 1, No. What is the probability of the occurrence of a number that is odd or less than 5 when a fair die is rolled. Consider making a small contribution. (i.e. having the side length of 1 unit = 7×(8 rows + 8 columns) = 112. Richard Durret has a text called Probability: theory and example that is amazing. Probability questions for S&T interview (Originally Posted: 04/01/2008) ... it was just expectation however it was near impossible to structure the answer. 98888--->number of 5 digit =5, Now for a 5 digit number of form (pqrst) to be divisible by, $11(p+r+t)−(q+s)=11$, also $(p+r+t)+(q+s)=41$, $(p,r,t)=(9,9,8)$ and $(q,s)=(8,7)$ --------(i), or $(p,r,t)=(9,9,8)$ and $(q,s)=(9,6)$  --------(ii), Hence, required probability = 12/70 = 6/35. In terms of probabilities, we know the following: \(P(A_1)=\dfrac{5}{365}=0.0136985\) [It rains 5 days out of the year. For a sequence of positive integers a1,a2,…,aka_{1},a_{2},\ldots,a_{k}a1​,a2​,…,ak​ , its value VVV …, If you take one coin from the box there is a 50% chance it’s a gold …. The questions here will cover the basics as well as the hard level problems for all levels of students. In recent years, it has rained only 5 days each year. Online Practice of these difficult problems on Probability will enable you to perform well in Aptitude Tests of various competitive examinations like CAT, XAT, MAT, GRE, GMAT, SAT, IRMA, FMS, IIFT, NMIMS etc. got it though after about 5 minutes of hard work and got the job. Difficult Probability Question - 9. The expected value of the number of throws, such that each of sums appears at least once, is AB \frac{ A}{B }BA​, …, Bob and Alice are playing a dice game. Why are the possibilities of rolling the dice for each number, this way : Below is the probability of rolling a certain number with two dice. Now there are 7 unique adjacent square sets in each row and each column. having the side length of 2 unit = 5×(7 rows + 7 columns) = 70 Sum of digits of a 5 digit number is 41. Unfortunately, the weatherman has predicted rain for tomorrow. Also, there could be other solution too if we consider ALL possible squares and not only the smallest squares. ‘2’ – 1/36 ‘3’ – 2/36 ‘4’ – 3/36 ‘5’- 4/36. 2020| Log in. In order to get the sum as 41, the following 5 digit combination exist: 99995--->number of 5 digits =5 © Lofoya Pvt Ltd. One from the total group, thus selected is selected as a leader at random. \(=\left(\dfrac{\text{Favourable cases}}{\text{Sample Space}}\right)\). The questions here will be provided, as per NCERT guidelines. Learn and practice basic word and conditional probability aptitude questions with shortcuts, useful tips to … Even when the weatherman predicts rain, it only rains only about $11\%$ of the time. 36, 3x3 squares Notation for these events appears below. It does not rain on Marie's wedding. Solution. The number of ways of choosing 4 squares from 64 is \(^{64}C_4\). New user? 4, 7x7 squares We want to know $P(A_1|B)$, the probability it will rain on the day of Marie's wedding, given a forecast for rain by the weatherman.