(i) Primes 7 and 11 give 8 pairs, P = 8/36 = 2/9. (ii) P(different) = 1 – P(same) = 1 – 13/36 = 23/36. (iii) Favourable outcomes {HHT, HTH}, P = 2/8 = 1/4. (iv) Last digit 2 or 4, P = ...
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For two dice, maximum sum is 12. An event with probability 0 is getting a sum of 13. An outcome or event with probability 1 is getting a sum between 2 and 12.
The marble counts represent the sum of the first 25 natural numbers. Using the sum formula Sn = n(n + 1) / 2 with n = 25, the total calculation is 25 x 26 / 2, which gives 325 marbles.
With initial salary of 5,00,000 and annual increment of 20,000, his earnings form an AP. Solving 7,00,000 = 5,00,000 + (n – 1) x 20,000 gives n = 11, meaning his income reaches 7,00,000 after 10 years.
The two-digit numbers divisible by 3 range from 12 to 99, forming an AP with common difference 3. There are 30 such numbers and applying the arithmetic sum formula gives a total sum of 1665.