Questions on Probability and Statistics
Sticky Ad Probability Problems with Detailed Solutions Click each question to expand the detailed interpretation and solution. Question 1: Two unbiased dice are thrown Two fair dice are rolled together. Find the probability that: (i) the sum is even (ii) the sum is less than 5 (iii) the sum is at most 12 Since each die has 6 possible outcomes, the total number of outcomes is: $$6\times6=36$$ We calculate the number of favorable outcomes for each condition. (i) Sum is even The sum is even when: both numbers are even both numbers are odd Number of even numbers on a die = 3 Number of odd numbers on a die = 3 $$3\times3+3\times3=18$$ Therefore, $$P(\text{sum is even})=\frac{18}{36}=\frac12$$ (ii) Sum is less than 5 Possible sums are 2, 3 and 4. Number of favorable outcomes: $$1+2+3=6$$ H...