13.1 theoretical probability

ProbabilityProbability

Student Study Guide13.1 Theoretical Probability

Student Study Guide13.1 Theoretical Probability

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

1. 14

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

1. 14

1501

50

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is2. Less than 37

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is2. Less than 37

36 numbers less than 3736 numbers less than 37

36 5036 50

= 18 25= 18 25

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

3. A perfect square

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

3. A perfect square1x1=1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36,

7x7=49, 8x8=64

1x1=1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36,

7x7=49, 8x8=647 507 50

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

4. Odd and less than 25

A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find

the probability that the number drawn is

4. Odd and less than 251, 3, 5, 7, 9, 11, 13, 15, 17, 19,

21, 231, 3, 5, 7, 9, 11, 13, 15, 17, 19,

21, 2312 5012 50

= 6 25= 6 25

A coin is tossed 3 times. Find each probability.

5. P(3 heads)

A coin is tossed 3 times. Find each probability.

5. P(3 heads)

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

1 81 8

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

A coin is tossed 3 times. Find each probability.

6. P(exactly 1 tails)

A coin is tossed 3 times. Find each probability.

6. P(exactly 1 tails)

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

3 83 8

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

A coin is tossed 3 times. Find each probability.

7. P(at least 1 heads)

A coin is tossed 3 times. Find each probability.

7. P(at least 1 heads)

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

7 87 8

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

A coin is tossed 3 times. Find each probability.

7. P(at least 1 heads)

A coin is tossed 3 times. Find each probability.

7. P(at least 1 heads)

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

7 87 8

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

A coin is tossed 3 times. Find each probability.

8. P(at least 2 heads)

A coin is tossed 3 times. Find each probability.

8. P(at least 2 heads)

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

4 84 8

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

= 1 2= 1 2

Practice Masters Level BPractice Masters Level B

13.1 Theoretical Probability13.1 Theoretical Probability

#2 - Sample Space#2 - Sample Space

2. Rolling a number cube and then tossing a coin

2. Rolling a number cube and then tossing a coin

1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T

1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T

2 x 6 = 122 x 6 = 12

2 sides on a coin6 sides on a cube2 sides on a coin6 sides on a cube

Find the number of favorable outcomes in the sample space

for each experiment. 4. A number cube is rolled

twice. The sum of the rolls is 6.

Find the number of favorable outcomes in the sample space

for each experiment. 4. A number cube is rolled

twice. The sum of the rolls is 6.

1+5, 5+1, 2+4, 4+2, 3+31+5, 5+1, 2+4, 4+2, 3+3

55

5 different options5 different options

Suppose that you select a letter of the English alphabet at random.

Find the probability of each event.7. The letter is in the word

Mississipi.

Suppose that you select a letter of the English alphabet at random.

Find the probability of each event.7. The letter is in the word

Mississipi.26 letters in the alphabet26 letters in the alphabet

4264

26

4 different letters4 different letters

m, i, s, pm, i, s, p

= 2 13= 2 13

Suppose that you select a letter of the English alphabet at random.

Find the probability of each event.8. The letter is in the word Ohio.

Suppose that you select a letter of the English alphabet at random.

Find the probability of each event.8. The letter is in the word Ohio.

26 letters in the alphabet26 letters in the alphabet

3263

26

3 different letters3 different letters

O, h, iO, h, i

Find the probability of each outcome.

14. Two rolls of a number cube will have a sum of 7.

Find the probability of each outcome.

14. Two rolls of a number cube will have a sum of 7.

1+6, 6+1, 3+4, 4+3, 2+5, 5+21+6, 6+1, 3+4, 4+3, 2+5, 5+2

6?6?

6 different combinations6 different combinations

14. Two rolls of a number cube will have a sum of 7.

14. Two rolls of a number cube will have a sum of 7.

36 possibilities

6x6=36

36 possibilities

6x6=36

1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,

6+6

1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,

6+6 636

Find the probability of each outcome.

15. Two tosses of a coin will be two heads.

Find the probability of each outcome.

15. Two tosses of a coin will be two heads.

14

HH, HT, TH, TTHH, HT, TH, TTHH, HT, TH, TTHH, HT, TH, TT

Find the probability of each outcome.

16. Two rolls of a number cube will have an odd sum.

Find the probability of each outcome.

16. Two rolls of a number cube will have an odd sum.

18 ?

Odd + Even number = Odd Sum

Odd + Even number = Odd Sum

1+2, 1+4, 1+6, 2+1, 2+3, 2+5, 3+2, 3+4, 3+6, 4+1, 4+3, 4+5, 5+2, 5+4, 5+6, 6+1, 6+3, 6+5

1+2, 1+4, 1+6, 2+1, 2+3, 2+5, 3+2, 3+4, 3+6, 4+1, 4+3, 4+5, 5+2, 5+4, 5+6, 6+1, 6+3, 6+5

16. Two rolls of a number cube will have an odd sum.

16. Two rolls of a number cube will have an odd sum.

36 possible outcomes

1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,

6+6

1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,

6+6 1836