Binomial Probability Problems

**Page 3**

21.

A survey was conducted in a class of 50 about the games the students play. Each student had to select only one particular game or no game. The results of the survey are: 20 play football, 15 play basketball and 10 play baseball. What is the probability that a student selected does not play any game?

a. | $\frac{3}{10}$ | ||

b. | Zero | ||

c. | $\frac{9}{10}$ | ||

d. | $\frac{1}{10}$ |

P(E) =

Total number of students in the class n(S) = 50

Number of students who do not play any games = Total number of students in the class - (Number of students who play football + Number of students who play basketball + Number of students who play baseball)

Number of students who do not play any games = 50 - (20 + 15 + 10)

Number of students who do not play any games = 50 - 45

Number of students who do not play any games n(E) = 5

P(E) =

[Substitute n(E) = 5 and n(S) = 50 in P(E).]

P(E) =

[Simplify.]

Probability that a selected student does not play any game is

Correct answer : (4)

22.

The distribution of the ages of the members of a colony is as follows :

If a person is selected at random, then find the probability that his/her age is less than 30 years.

Age | Frequency |

0 - 20 | 35 |

21 - 30 | 15 |

31 - 40 | 20 |

41 - 50 | 25 |

51 - 60 | 15 |

61 - up | 10 |

a. | $\frac{5}{12}$ | ||

b. | $\frac{1}{8}$ | ||

c. | $\frac{7}{12}$ | ||

d. | $\frac{7}{24}$ |

P(E) =

Total frequencies in the distribution = 35 + 15 + 20 + 25 + 15 + 10

Frequency for the class 0 - 30 = Frequency for the class 0 - 20 + Frequency for the class 21 - 30

P(E) =

[Substitute the values of

P(E) =

[Simplify.]

Probability that a person selected is less than 30 years is

Correct answer : (1)

23.

The distribution of the ages of the members of a colony is as follows :

If a person is selected at random, then find the probability that his/her age is over 41 years and under 60.

Age | Frequency |

0 - 20 | 35 |

21 - 30 | 15 |

31 - 40 | 20 |

41 - 50 | 25 |

51 - 60 | 15 |

61 - up | 10 |

a. | $\frac{1}{8}$ | ||

b. | $\frac{1}{3}$ | ||

c. | $\frac{5}{12}$ | ||

d. | $\frac{5}{24}$ |

P(E) =

Total frequencies in the distribution = 35 + 15 + 20 + 25 + 15 + 10

Frequency for the class 41 - 60 = Frequency for the class 41 - 50 + Frequency for the class 51 - 60

P(E) =

[Substitute the values of

P(E) =

[Simplify.]

Probability that a person selected is over 41 and under 60 is

Correct answer : (2)

24.

Specify the nature of probability that the following statement denotes:

The probability that it will rain tomorrow is 83%( Weather Department Forecast).

The probability that it will rain tomorrow is 83%( Weather Department Forecast).

a. | Cannot be determined | ||

b. | Empirical probability | ||

c. | Classical probability | ||

d. | Subjective probability |

The probability statement given is based on professional information and experience.

So, the statement denotes empirical probability.

Correct answer : (2)

25.

Specify the nature of probability that the following statement denotes:

The probability of drawing an Ace from a pack of 52 cards is $\frac{1}{13}$.

The probability of drawing an Ace from a pack of 52 cards is $\frac{1}{13}$.

a. | Subjective probability | ||

b. | Classical probability | ||

c. | Cannot be determined | ||

d. | Empirical probability |

In the probability statement each outcome has equal probability to occur.

So, the statement denotes classical probability.

Correct answer : (2)

26.

What type of probability does the statement denote?

The probability that a student will get 60% and above is 0.23.

The probability that a student will get 60% and above is 0.23.

a. | Subjective probability | ||

b. | Classical probability | ||

c. | Empirical probability | ||

d. | Cannot be determined |

Probability statement given is based on professional information and experience.

So, the statement denotes empirical probability.

Correct answer : (3)

27.

Specify the nature of probability that the following statement denotes:

The probability that a new motel venture in the State will succeed is 25%.

The probability that a new motel venture in the State will succeed is 25%.

a. | Empirical probability | ||

b. | Classical probability | ||

c. | Cannot be determined | ||

d. | Subjective probability |

The probability statement is based on professional information and experience.

So, the statement denotes empirical probability.

Correct answer : (1)

28.

Identify the nature of probability in the statement:

The probability that a patient suffers from viral fever is 0.7 (Hospital Diagnosis).

The probability that a patient suffers from viral fever is 0.7 (Hospital Diagnosis).

a. | Subjective probability | ||

b. | Cannot be determined | ||

c. | Classical probability | ||

d. | Empirical probability |

Probability is based on professional information and experience.

So, the statement denotes empirical probability.

Correct answer : (4)

29.

The Sample Space (S) derived from drawing 2 students from a group of 2 Boys B_{1}, B_{2} and 3 Girls G_{1}, G_{2}, G_{3} is:

a. | { B _{1}B_{2}, G_{1}G_{2}, G_{1}G_{3}, G_{2}G_{3} } | ||

b. | { B _{1}B_{2}, B_{1}G_{1}, B_{1}G_{2}, B_{1}G_{3}, B_{2}G_{1}, B_{2}G_{2}, B_{2}G_{3}, G_{1}G_{2}, G_{1}G_{3}, G_{2}G_{3} } | ||

c. | { B _{1}G_{1}, B_{1}G_{2}, B_{1}G_{3}, B_{2}G_{1}, B_{2}G_{2}, B_{2}G_{3} } | ||

d. | { B _{1}B_{2}, B_{1}G_{1}, B_{1}G_{2}, B_{1}G_{3}, B_{2}G_{1}, B_{2}G_{2}, B_{2}G_{3} } |

The sample space is: { B

Correct answer : (2)

30.

A coin and a die are rolled. The sample space(S) of getting a Head(H) on the coin and an even number on the die is:

a. | S = { (H, 2) (H, 4) (H, 6) (T, 2) (T, 4) (T, 6) } | ||

b. | S = { (H, 2) (H, 4) (H, 6) } | ||

c. | S = { (H, 1) (H, 2) (H, 3) (H, 4) (H, 5) (H, 6) (T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (H, 6) } | ||

d. | S = { (H, 1) (H, 2) (H, 3) (H, 4) (H, 5) (H, 6) } |

The sample space is: S = { (H, 2) (H, 4) (H, 6) }.

Correct answer : (2)