7.5.0: Exercises

For the following exercises, we are considering two special 6-sided dice. Each face is labeled with a number and a letter: the first die has faces 1A, 1B, 2A, 2C, 4A, 4E; the second has faces 1A, 1A, 2A, 2B, 3A, 3C. Assume that each face has an equal probability of landing face up.

Exercise \(\PageIndex{1}\)

Use a table to identify the sample space of the experiment in which we roll both dice and note the sum of the two numbers that are showing.

Exercise \(\PageIndex{2}\)

What is the probability that we roll a sum less than 8?

Exercise \(\PageIndex{3}\)

What is the probability that we roll a sum larger than 8?

Exercise \(\PageIndex{4}\)

What is the probability that we roll a sum less than or equal to 2?

Exercise \(\PageIndex{5}\)

What is the probability that we roll a sum greater than 2?

Exercise \(\PageIndex{6}\)

What is the probability that we roll an even sum?

Exercise \(\PageIndex{7}\)

What is the probability that we roll an odd sum?

Exercise \(\PageIndex{8}\)

Use a table to identify the sample space of the experiment in which we roll both dice and note the two letters that are showing.

Exercise \(\PageIndex{9}\)

What is the probability that no As are showing?

Exercise \(\PageIndex{10}\)

What is the probability that at least one A is showing?

Exercise \(\PageIndex{11}\)

What is the probability that two As are showing?

Exercise \(\PageIndex{12}\)

What is the probability that two of the same letter are showing?

Exercise \(\PageIndex{13}\)

What is the probability that the letter on the first die comes alphabetically before the letter on the second die?

Exercise \(\PageIndex{14}\)

What is the probability that two vowels are showing?

Exercise \(\PageIndex{15}\)

What is the probability that two consonants are showing?

Exercise \(\PageIndex{16}\)

What is the probability that one consonant and one vowel are showing?

In the following Exercises, decide whether the given probability was likely determined theoretically, empirically, or subjectively.

Exercise \(\PageIndex{17}\)

Carolyn is breeding two pea plants, and notes that 8 of the 25 offspring plants have yellow peas. So, she concludes that there’s a 32% chance that an offspring of these two plants will have yellow peas.

Exercise \(\PageIndex{18}\)

At the beginning of the semester, Malik estimates there’s a 30% chance that he’ll earn As in all his classes.

Exercise \(\PageIndex{19}\)

Abbie is deciding where she will attend college in the fall. Right now, she thinks there’s an 80% chance she’ll attend an in-state school.

Exercise \(\PageIndex{20}\)

If you roll three standard 6-sided dice, the probability that the sum will be 8 is \(\frac21216\).

Exercise \(\PageIndex{21}\)

According to the app he uses to play the game, Jason has won 18 of the last 100 games of solitaire he’s played. So, the probability that he wins the next one is about 18%.

Exercise \(\PageIndex{22}\)

Jim and Anne are both in a club with 10 members. If 3 people are chosen at random to form a committee, then the probability that both Jim and Anne are chosen is \(\frac{1}15\).

For the following exercises, use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter’s opportunity to try to get a hit. The other columns are runs scored (R), hits (H), doubles (2B), triples (3B), home runs (HR), walks (BB), and strike outs (SO).

Name	Team	PA	R	H	2B	3B	HR	BB	SO
Marcus Semien	OAK	747	123	187	43	7	33	87	102
Whit Merrifield	KCR	735	105	206	41	10	16	45	126
Ronald Acuna Jr.	ATL	715	127	175	22	2	41	76	188
Jonathan Villar	BAL	714	111	176	33	5	24	61	176
Mookie Betts	BOS	706	135	176	40	5	29	97	101
Rhys Hoskins	PHI	705	86	129	33	5	29	116	173
Jorge Polanco	MIN	704	107	186	40	7	22	60	116
Rafael Devers	BOS	702	129	201	54	4	32	48	119
Ozzie Albies	ATL	702	102	189	43	8	24	54	112
Eduardo Escobar	ARI	699	94	171	29	10	35	50	130
Xander Bogaerts	BOS	698	110	190	52	0	33	76	122
José Abreu	CHW	693	85	180	38	1	33	36	152
Pete Alonso	NYM	693	103	155	30	2	53	72	183
Freddie Freeman	ATL	692	113	176	34	2	38	87	127
Alex Bregman	HOU	690	122	164	37	2	41	119	83

Exercise \(\PageIndex{23}\)

Mookie Betts gets a home run in his next plate appearance.

Exercise \(\PageIndex{24}\)

Xander Bogaerts strikes out in his next plate appearance.

Exercise \(\PageIndex{25}\)

Jonathan Villar gets a hit in his next plate appearance.

Exercise \(\PageIndex{26}\)

Rhys Hoskins gets a walk in his next plate appearance.

Exercise \(\PageIndex{27}\)

José Abreu scores a run in his next plate appearance.

Exercise \(\PageIndex{28}\)

Eduardo Escobar hits a triple in his next plate appearance.

Exercise \(\PageIndex{29}\)

Whit Merrifield hits a double in his next plate appearance.

Exercise \(\PageIndex{30}\)

Ronald Acuna Jr. gets an extra-base hit (double, triple, or home run) in his next plate appearance.

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