For 1-3, consider a box filled with 30 red balls and 70 white balls. You randomly
draw out a ball 4 times and replace it each
time. Drawing out a red ball is considered
a success.
1. Complete the table with the probability of
choosing each number of red balls
2. Draw a histogram of the distribution.
3. Choose True or False for each statement
about the distribution
A The probability of choosing a red ball
2 or more times is 0.3483
O True False
B The probability of choosing a red ball
at least 2 times is 0.6517.
True False
C The probability of choosing a red ball
at least 3 times is 0.0837
O True False

triangle and cube

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt