Probability Worksheets

**Page 2**

11.

Which of the following are dependent events?

1. Getting an even number in the first roll of a number cube and getting an even number in the second roll.

2. Getting an odd number on the number cube and spinning blue color on the spinner.

3. Getting a face card in the first draw from a deck of playing cards and getting a face card in the second draw. (The first card is not replaced)

1. Getting an even number in the first roll of a number cube and getting an even number in the second roll.

2. Getting an odd number on the number cube and spinning blue color on the spinner.

3. Getting a face card in the first draw from a deck of playing cards and getting a face card in the second draw. (The first card is not replaced)

a. | 2 | ||

b. | 1 and 3 | ||

c. | 3 | ||

d. | 2 and 3 |

In (2), rolling an odd number and spinning blue color are two independent events.

In (3), since the first card is not replaced back, the probability of the second draw depends on the first draw.

So, the two events in (3) are dependent events.

Correct answer : (3)

12.

Two cards are drawn from a set of 10 cards numbered from 1 to 10, without replacing the first card. What is the probability that both the cards have prime numbers on them?

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

b. | $\frac{2}{15}$ | ||

c. | $\frac{4}{15}$ | ||

d. | $\frac{1}{15}$ |

P(1

[Substitute and simplify the fraction.]

Since one prime number is selected, the second prime number is to be selected from the remaining 3 primes.

The two events are dependent events.

[Since the first card is not replaced.]

P(2

[Substitute and simplify the fraction.]

P(two prime numbers) = P(1

[Substitute and multiply.]

So, the probability that both the selected cards have prime numbers is

Correct answer : (2)

13.

Two cards are drawn one after the other from a standard deck of cards. Find the probability of drawing a black card and then a red card.

a. | $\frac{13}{51}$ | ||

b. | $\frac{1}{169}$ | ||

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

d. | $\frac{26}{51}$ |

P(black card) =

Since the first black card drawn is not replaced back, the total number of cards reduces by one.

P(red card) =

P(black card first, red card next) = P(black card) × P(red card)

=

[Substitute and simplify the product.]

The probability of drawing a black card and then a red card is

Correct answer : (1)

14.

A football team coach needs two more players to form a team. There are 15 boys ready to play but out of them only 5 are good and the remaining are average players. What is the probability that the two players selected are good players?

a. | $\frac{1}{11}$ | ||

b. | $\frac{3}{22}$ | ||

c. | $\frac{1}{7}$ | ||

d. | $\frac{2}{21}$ |

[Substitute.]

Since the first player selected should not be selected again, total number of players reduces by one.

P(selecting second good player) =

[Substitute.]

P(both good players) = P(selecting first good player) × P(selecting second good player)

=

[Substitute and simplify the product.]

Probability that the two players selected are good players is

Correct answer : (4)

15.

There are 10 pens and 12 pencils in a box. If a student selects two of them at random, then what is the probability of selecting a pen and then a pencil?

a. | $\frac{20}{77}$ | ||

b. | $\frac{157}{308}$ | ||

c. | $\frac{137}{231}$ | ||

d. | $\frac{214}{231}$ |

Total number of pens and pencils = 10 + 12 = 22

P(pen) =

[Substitute.]

Since a pen is already selected, total number of pens and pencils is reduced by one.

P(pencil) =

[Substitute.]

P(a pen, then a pencil) = P(pen) × P(pencil)

=

[Substitute and simplify the product.]

Probability of a student selecting a pen and then a pencil is

Correct answer : (1)

16.

Chris draws a card from a pack of cards and also throws a dice. What is the probability of Chris drawing a king and getting a number less than 4?

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

b. | $\frac{25}{26}$ | ||

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

d. | $\frac{3}{26}$ |

Probability of Chris drawing a king = P(a king) =

When a dice is thrown, 1, 2, 3 are the numbers that are less than 4.

Total number of outcomes when a dice is thrown = 6

Probability of Chris getting a number less than 4 when the dice is thrown = P(number less than 4) =

Drawing a card and throwing a dice are independent events.

P(a king and number less than 4) = P(a king) × P(number less than 4)

=

[Substitute and multiply the two probabilities.]

So, the probability of Chris drawing a king and getting a number less than 4 is

Correct answer : (3)

17.

A dice is rolled twice. What is the probability of getting the product of the numbers rolled greater than 35?

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

b. | $\frac{35}{36}$ | ||

c. | 1 | ||

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

Total number of possible outcomes when a dice is rolled twice = 36

[Since there are 6 outcomes when a dice is rolled once, there are (6 x 6) outcomes when the dice is rolled twice.]

Number of outcomes in which the product of the numbers rolled is greater than 35 = 1

[(6, 6) is the only outcome with the product of the numbers rolled being greater than 35.]

P(product > 35) =

The probability of getting the product of the numbers rolled greater than 35 is

Correct answer : (4)

18.

A magician holds a pack of 52 cards in his hand. If he takes two cards from the pack one after the other, then what is the probability that the two cards drawn are number cards?

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

b. | $\frac{1}{18}$ | ||

c. | $\frac{105}{221}$ | ||

d. | $\frac{108}{221}$ |

Probability of selecting the first card =

The second card is to be selected from the remaining 51 cards out of which, 35 are number cards.

Probability of selecting the second card =

Probability that the two cards are number cards =

[Substitute and simplify.]

Correct answer : (3)

19.

Sam and Dennis draw a card each from a deck of playing cards, one after the other, with replacement. What is the probability of Sam drawing a face card and then Dennis drawing a number card?

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

b. | $\frac{3}{221}$ | ||

c. | $\frac{36}{169}$ | ||

d. | $\frac{16}{169}$ |

Since the first card drawn is replaced, the two events are independent events.

P(Sam drawing a face card) =

P(Dennis drawing a number card) =

P(Sam drawing a face card and then Dennis drawing a number card) = P(Sam drawing a face card) × P(Dennis drawing a number card)

=

[Substitute the two probabilities and simplify.]

So, the probability of Sam drawing a face card and then Dennis drawing a number card is

Correct answer : (3)

20.

Tim has a basket of 2 apples, 4 oranges, and 7 peaches. He wants to pack three fruits in a small box. Find the number of different fruit combinations Tim can make.

a. | 3 | ||

b. | 17 | ||

c. | 56 | ||

d. | 15 |

Correct answer : (3)