Probability

A non-leap year has 365 days. We know that there are 52 weeks in a year, which accounts for days. So, a non-leap year has 52 full weeks and 1 extra day. For a non-leap year to have 53 Sundays, this extra day must be a Sunday. The extra day can be any one of the 7 days of the week: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday. Each of these 7 days has an equal probability of being the extra day. The probability that the extra day is a Sunday is 1 out of 7 possible days. Therefore, the probability that a non-leap year will have 53 Sundays is .

Total number of balls in the bag balls. We are drawing three balls in succession. We need to find the probability of the event where the first ball is red, the second ball is black, and the third ball is white. Probability of the first ball being red: Number of red balls Total number of balls After drawing one red ball, there are now 9 balls left in the bag: 5 black, 3 white, and 1 red. Probability of the second ball being black (given the first was red): Number of black balls Total number of remaining balls After drawing one red and one black ball, there are now 8 balls left in the bag: 4 black, 3 white, and 1 red. Probability of the third ball being white (given the first was red and the second was black): Number of white balls Total number of remaining balls The probability of all three events occurring in this sequence is the product of their individual probabilities: $ $ Therefore, the probability that the first ball is red, the second ball is black, and the third ball is white is .

When two dice are tossed, total possible outcomes = . We look for pairs such that . The favorable pairs are: There are 4 favorable outcomes. Hence, probability = .