Assignment 2
Topics: Lecture 4, 7, 8
Lecture 4:
1. What is the coefficient of x47 is the expansion of (2x3+ 1𝑥)29 ? [if the answer has a form like 29Ca*bk, what is the value of (a+b+k) ?
2. The 3rd term in the expansion of (y2+2/y)21 and the 3rd term in the expansion of
(y+⅓)37 are equal. What is the value of y? [Give the answer in fractional form]
3. What is the coefficient of z4in the expansion of(z3+3z+1)6?
4. What is the coefficient of a5b3c2 in the expansion of (370a+285b+99c)11?
Lecture 7:
1. Two dice are tossed. What is the probability that the total score is a prime number greater than 3?
2. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. What is the probability that at least one of these is defective?
3. Four cards are drawn from a standard deck of playing cards without replacing a card after it is drawn. If the first 3 cards are spades, what is the probability that the next card drawn is not a spade?
4. 4 ETS big book and 5 barrons books are arranged in a row on a shelf at random. Find the probability that the books of the same publisher will be put together?
Lecture 8:
1. An n sided die is rolled. Each face has a unique label from 1 to n. Let, X be the random variable that denotes the number that is on top of the die after it has landed. Express the variance of the variable X in terms of n.
2. An n sided die is rolled. Each face has a unique label from 1 to n. Let, X be the random variable that denotes the number that is on top of the die after it has landed. Determine P r(X ≤ n).
3. Two 10 sided dice are rolled. What is the probability that the sum of the two numbers that come up on the dice is a prime number?
4. Two n sided die are cast. Each faces are numbered from 1 to n. One die is red, one is blue. What is the probability that the red one doesn’t land a number divisible by 3 and the blue one doesn’t land a number divisible by 2?
