Independent Events Worksheets

**Page 1**

1.

A box consists cards labeled 1 through 10. A card is drawn at random and replaced. Then a second card is drawn. Find the probability that the first number is odd and the second number is a multiple of 3.

a. | 0.08 | ||

b. | 1.5 | ||

c. | 0.15 | ||

d. | 0.8 |

[There are 5 odd numbers: 1, 3, 5, 7, 9.]

P (2

[There are 3 multiples of three: 3, 6, 9.]

P (1

= P (1

=

=

=

The probability that the first number is odd and the second number is a multiple of 3 is 0.15.

Correct answer : (3)

2.

A box consists cards labeled 1 through 10 written on them. A card is drawn at random and replaced. Then a second card is drawn. Find the probability that the first number is less than 5 and second number is a prime number.

a. | 1.6 | ||

b. | 0.08 | ||

c. | 0.8 | ||

d. | 0.16 |

[There are 4 numbers that are less than 5 : 1, 2, 3, 4]

P (2

[There are 4 prime numbers : 2, 3, 5, 7.]

P (1

=

= 0.16

The probability that the first number is less than 5 and second number is a prime number is 0.16.

Correct answer : (4)

3.

The probability that A gets a fellowship is 0.3 and B gets fellowship is 0.8. Find the probability that both A and B get fellowship.

a. | 0.24 | ||

b. | 0.14 | ||

c. | 0.11 | ||

d. | 2.4 |

P(B gets fellowship) = 0.8

P(A and B get fellowship) = P(A gets fellowship) × P(B gets fellowship)

[A and B are independent events.]

= 0.3 × 0.8 = 0.24

Correct answer : (1)

4.

If P(A) = 0.1, P(B) = 0.4 and P(A$\cap $B) = 0.2, then find P(A$\cup $B)

a. | 0.3 | ||

b. | 0.7 | ||

c. | 0.5 | ||

d. | 0.6 |

[P (A

= 0.3

Correct answer : (1)

5.

If S is a sample space and A, B and C are mutually exclusive, then P(A$\cup $B$\cup $C) = ?

a. | 1 | ||

b. | P (A) + P (B) + P(C) - P(A$\cap $B$\cap $C) | ||

c. | P (A) + P (B) + P(C) |

= P (A) + P (B) + P(C).

[ A, B and C are mutually exclusive.

P (A

Correct answer : (3)

6.

If P (A) = 0.6, then P ($\stackrel{\u203e}{A}$) = ?

a. | 0.4 | ||

b. | 0.6 | ||

c. | 1 |

= 1 - 0.6

= 0.4

Correct answer : (2)

7.

If P ($\stackrel{\u203e}{E}$) = 0.02, then P (E) = ?

a. | 0.08 | ||

b. | 0.98 | ||

c. | 0.02 | ||

d. | 0.8 |

= 1 - 0.02

= 0.98

Correct answer : (2)

8.

If P(A) = 0.3, P(A$\cap $B) = 0.06 and the events A and B are independent, then find P(B)?

a. | 0.2 | ||

b. | 0.02 | ||

c. | 0.24 | ||

d. | 0.03 |

[A and B are independent events.]

0.06 = 0.3 × P(B)

0.2 = P(B)

Correct answer : (1)

9.

If P (A) = 0.25 and P (B) = 0.5, then find P(A$\cap $B), if A and B are independent events.

a. | 1.25 | ||

b. | 0.3 | ||

c. | 0.75 | ||

d. | 0.125 |

[P(A

= 0.125

Correct answer : (4)

10.

A box consists cards labeled numbers 1 through 10. A card is drawn at random and replaced. Then a second card is drawn. Find the probability that the first number drawn is 5 and the second number is 10.

a. | 0.1 | ||

b. | 0.01 | ||

c. | 1 | ||

d. | 0.2 |

P(A) =

Let B be the event of getting a number 10.

P(B) =

P(the first number is 5 and the second number is 10) = P(A

= P(A) × P(B)

[A and B are independent events.]

=

=

The probability that the first number drawn is 5 and the second number is 10 is 0.01.

Correct answer : (2)

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