True or false, and explain: (a) if a die is rolled three times, the chance of getting at least one ace is 1/6 + 1/6 + 1/6 = 1/2. (b) if a coin is tossed twice, the chance of getting at least one head is 100%.

a.False

b.False

Step-by-step explanation:

a.Total possible outcomes of a die=1,2,3,4,5,6=6

Probability of getting an ace=

Favorable cases=1

Probability of getting an ace=

A die is rolled three times .

We are given that the probability of getting at least one ace is

There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .

The events are mutually exclusive when the events cannot occur at the same time.

Since it is possible to obtain one ace on more than one roll of a die.

Therefore, the events are not  mutually exclusive.

Hence, the given statement is false.

b.Total cases in one coin=2(H,T)

Number of cases in favor of head=1

The probability of getting on head=

The coin is tossed twice.

We are given that

If a coin is tossed twice ,the chance of getting at least on head is 100%.

There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .

The events are mutually exclusive when the events cannot occur at the same time.

Since it is possible to obtain head on both  tosses of coin.

Therefore, the events are not  mutually exclusive.

Hence, the given statement is false.

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: