Probability Worksheets

**Page 5**

41.

Find the odds in favor of getting exactly 1 head when three coins are tossed.

a. | 2 : 1 | ||

b. | 5 : 3 | ||

c. | 3 : 5 | ||

d. | 1 : 2 |

The odds in favor of getting exactly 1 head are 3 : 5

[Three outcomes are successes and 5 are failures.]

Correct answer : (3)

42.

A box contains 20 cards labeled 1 through 20. One card is drawn from it at random. Identify the event of drawing a card of an odd number.

a. | {11, 13, 15, 17, 19} | ||

b. | {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} | ||

c. | {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} | ||

d. | {1, 3, 5, 7, 9} |

Let A be the event of drawing a card of an odd number.

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

The event of drawing a card of an odd number is {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.

Correct answer : (3)

43.

A box contains 20 cards labeled 1 through 20 on them. One card is drawn from it at random. Write the event of drawing a multiple of 5.

a. | {5, 10, 15, 20} | ||

b. | {5, 10} | ||

c. | {5, 15} | ||

d. | {1, 5, 10, 20} |

Let B be the event of drawing a card whose number is a multiple of 5.

B = {5, 10, 15, 20}

The event of drawing a card whose number is a multiple of 5 is B = {5, 10, 15, 20}

Correct answer : (1)

44.

Fifteen cards labeled A through O are placed in a bag. The bag is shaken and one card is drawn at random. Write the event of drawing a consonant.

a. | {A, B, C, D, E, F, G, H, I, J} | ||

b. | {B, C, D, F, G, H, J, K, L, M, N} | ||

c. | {B, C, D, F, G, H, I, J, K, L, M} | ||

d. | {A, E, I, O} |

Q = {B, C, D, F, G, H, J, K, L, M, N}

Correct answer : (2)

45.

What is the probability of getting a red card from a 52-card deck?

a. | $\frac{1}{26}$ | ||

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

c. | $\frac{1}{13}$ | ||

d. | $\frac{1}{4}$ |

[There are 26 red cards.]

Correct answer : (2)

46.

If two dice are rolled, then what is the probability that the sum of the dots will be 8?

a. | $\frac{5}{36}$ | ||

b. | $\frac{1}{9}$ | ||

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

d. | $\frac{5}{6}$ |

Let E be the event of getting the sum of dots is 8.

E = {(6, 2), (5, 3), (4, 4), (3, 5), (2, 6)}

The number of outcomes in E = 5

P(E) =

=

Correct answer : (1)

47.

Four cards are drawn from a bridge deck. What is the probability that all are diamonds?

a. | $\frac{4}{13}$ | ||

b. | $\frac{11}{4165}$ | ||

c. | $\frac{1}{4}$ | ||

d. | $\frac{1}{13}$ |

The number of outcomes in S is

Let E be the event of getting 4 diamonds from 13 in the deck.

The number of outcomes in E is

P(E) =

=

Correct answer : (2)

48.

Two dice are rolled. What is the probability that the sum of the dots showing will be less than 8?

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

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

c. | $\frac{13}{18}$ | ||

d. | $\frac{5}{9}$ |

Let E be the event of getting a sum less than 8 on the two dice.

E = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1)}

Number of outcomes in E = 21

P(E) =

=

Correct answer : (2)

49.

There are 12 boys and 10 girls. If 7 of them are selected at random, what is the probability that 4 are boys and 3 are girls?

a. | $\frac{{}_{7}{\mathrm{C}}_{3}}{{}_{12}{\mathrm{C}}_{4}}$ | ||

b. | $\frac{{}_{12}{\mathrm{C}}_{7}}{{}_{22}{\mathrm{C}}_{7}}$ | ||

c. | $\frac{({}_{12}{\mathrm{C}}_{4})({}_{10}{\mathrm{C}}_{3})}{{}_{22}{\mathrm{C}}_{7}}$ | ||

d. | $\frac{7}{22}$ |

Number of girls = 10

Total number of students = 22

The number of ways of selecting 7 from 22 is

So, the number of outcomes in sample space is

Let E be the event of selecting 4 boys from 12 and 3 girls from 10.

Number of outcomes in E =

P(E) =

=

Correct answer : (3)

50.

Two dice are rolled. What is the probability that both the dice show the same number of dots?

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

b. | 1 | ||

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

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

Let E be the event of getting the same number of dots on both the dice.

E = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

Number of outcomes in E = 6

P(E) =

=

Correct answer : (1)