Exam 11: Sequences, Series, and Probability

Find the probability of the event. -If you are dealt two cards successively (without replacement) from a standard 52-card deck, find the probability of getting a black on the first card and a heart on the second.

Solve the problem. -Suppose there are 7 roads connecting town A to town B and 3 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

Find the required part of the geometric sequence. -Find a formula for the nth term of a geometric sequence with third term and sixth term - .

Solve. -In how many ways can 8 people line up for play tickets?

List all equally likely outcomes in the sample space for the indicated experiment. -A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula. -

Write the series in summation notation. Use the index i and let i begin at 1 in each summation. -0 + 2 + 6 + 12 + 20

Identify the sequence as arithmetic, geometric, or neither. -7, 9, 13, 19, 27, . . .

Find the first five terms of the arithmetic sequence. -

Find the indicated part of the arithmetic sequence. -Find a formula for given that

Find the common ratio for the geometric sequence. -

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula. -

Solve the problem. -The kings are separated from a deck of standard playing cards and shuffled. One is randomly selected. What are the odds in favor of drawing a black card?

Find the probability of the event. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4?

Provide an appropriate response. -Consider the arrangements of sixteen students in a line. Are these combinations, permutations, or neither?

Use mathematical induction to prove the statement is true for all positive integers n. -

Solve the problem. -A football player with a field goal kicking percentage of 80% for kicks of 40 yards or less attempts a final-minute field goal of 32 yards. What are the odds in favor of a successful kick?

Find the sum of the series. -

Find the common ratio for the geometric sequence. -

Solve the problem. -Using the numerals 0 through 9, how many 6-digit serial numbers can be made if the first digit must be 0 or 1 and no numerals may be repeated?