Binomial Probability Problems

**Page 2**

11.

When a single die is rolled, what is the probability of getting an even prime number?

a. | $\frac{1}{2}$ | ||

b. | one | ||

c. | $\frac{1}{6}$ | ||

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

P(E) =

Sample space = { 1, 2, 3, 4, 5, 6 }

Number of elements in the sample space n(S) = 6

Even prime number in the given set = { 2 }

Number of even prime numbers n(E) = 1

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability of getting an even prime number when a single die is rolled is

Correct answer : (3)

12.

If 2 dice are rolled once, then what is probability of getting a sum of 1?

a. | $\frac{1}{6}$ | ||

b. | one | ||

c. | zero | ||

d. | $\frac{1}{36}$ |

P(E) =

Sample space for rolling two dice is

Number of elements in the sample space n(S) = 36

From the table, we see that we can never get a sum of 1. The minimum sum that can be obtained is 2. So n(E) = 0

P(E) = 0.

[Substitute the values of n(E) and n(S) in P(E).]

Probability of getting a sum of 1 when 2 dice are rolled once is 0.

Correct answer : (3)

13.

When a single die is rolled, what is the probability of getting an odd number greater than 3?

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

b. | $\frac{1}{6}$ | ||

c. | $\frac{1}{2}$ | ||

d. | zero |

P(E) =

Sample space = { 1, 2, 3, 4, 5, 6 }

Number of elements in the sample space n(S) = 6

Numbers greater than 3 in the sample space = { 4, 5, 6 }

Odd numbers in this set = { 5 }

Number of odd numbers which are greater than 3, n(E) = 1

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability of getting an odd number greater than 3, when a single die is rolled is

Correct answer : (2)

14.

If 2 dice are rolled once, then what is probability of getting a sum of 12?

a. | zero | ||

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

c. | $\frac{1}{6}$ | ||

d. | $\frac{1}{36}$ |

P(E) =

Sample space for rolling two dice is

Number of elements in the sample space n(S) = 36

From the table, we see that to get a sum of 12 both the dice should roll 6. So n(E) = 1

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability of getting a sum of 12 when 2 dice are rolled once is

Correct answer : (4)

15.

What is the probability that a selected alphabet is a vowel?

a. | $\frac{3}{13}$ | ||

b. | $\frac{21}{26}$ | ||

c. | $\frac{5}{26}$ | ||

d. | $\frac{2}{13}$ |

P(E) =

Sample space of alphabets = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }

Number of elements in the sample space n(S) = 26

Vowels = { a, e, i, o, u }

Number of vowels n(E) = 5

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability that a selected alphabet is a vowel is

Correct answer : (3)

16.

What is the probability that a selected alphabet is a consonant?

a. | $\frac{19}{26}$ | ||

b. | $\frac{21}{26}$ | ||

c. | one | ||

d. | $\frac{5}{26}$ |

P(E) =

Sample space of alphabets = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }

Number of elements in the sample space n(S) = 26

Consonants = { b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z }

Number of consonants n(E) = 21

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability that a selected alphabet is a consonant is

Correct answer : (2)

17.

If the probability that it will rain tomorrow is 0.6, then what is the probability that it will not rain tomorrow ?

a. | 0.5 | ||

b. | 0.4 | ||

c. | one | ||

d. | 0.6 |

P(E) + P(

0.6 + P(

[Substitute P(E) = 0.6.]

P(

P(

So, the probability that it will not rain tomorrow is 0.4.

Correct answer : (2)

18.

A college committee consisted of 4 boys and 3 girls. If a member is selected at random, then what is the probability that the selected member is a boy?

a. | $\frac{4}{7}$ | ||

b. | $\frac{3}{4}$ | ||

c. | $\frac{3}{7}$ | ||

d. | one |

P(E) =

Number of elements in Sample space = Number of boys + Number of girls.

n(S) = 4 + 3

n(S) = 7

Number of boys n(E) = 4

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

Probability that member selected is a boy is

Correct answer : (1)

19.

Specify the nature of probability that the following statement denotes:

The probability that the twin children born to a mother are both boys is $\frac{1}{3}$.

The probability that the twin children born to a mother are both boys is $\frac{1}{3}$.

a. | Cannot be determined | ||

b. | Classical probability | ||

c. | Empirical probability | ||

d. | Subjective probability |

In the given statement outcome has equal probability to occur.

So,the statement denotes classical probability.

Correct answer : (2)

20.

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 plays football?

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

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

c. | $\frac{2}{5}$ | ||

d. | $\frac{3}{5}$ |

P(E) =

Total number of students n(S) = 50

Number of students who play football n(E) = 20

P(E) =

[Substitute the values of n(E) and n(S) in P(E).]

P(E) =

[Simplify.]

Probability that a selected student plays football is

Correct answer : (3)