Probability Worksheets

**Page 3**

21.

If the event B depends on the event A, then P(B|A) =

a. | $\frac{\mathrm{P}(\mathrm{A}and\mathrm{B})}{\mathrm{P}(\mathrm{A})}$ | ||

b. | $\frac{\mathrm{P}(\mathrm{A}or\mathrm{B})}{\mathrm{P}(\mathrm{A})}$ | ||

c. | $\frac{\mathrm{P}(\mathrm{A}and\mathrm{B})}{\mathrm{P}(\mathrm{B})}$ | ||

d. | $\frac{\mathrm{P}(\mathrm{A}or\mathrm{B})}{\mathrm{P}(\mathrm{B})}$ |

[Conditional Probability Formula.]

Correct answer : (1)

22.

A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a spade and the second card is a club if the first card is not replaced.

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

b. | $\frac{13}{102}$ | ||

c. | $\frac{51}{52}$ | ||

d. | $\frac{13}{204}$ |

After the event of drawing a spade, the deck has 51 cards, of which 13 are clubs(C).

Therefore, P(C|S) =

Hence, P(S and C) = P(S) · P(C|S)

[Conditional Probability.]

= (

=

Correct answer : (4)

23.

Two dice were thrown and it is known that the numbers which come up were different. Find the probability that the sum of the two numbers was 4.

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

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

c. | $\frac{1}{30}$ | ||

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

There are two outcomes (3, 1) and (1, 3) in which the sum is 4 and the numbers are different. Hence,

P(B|A) =

[Conditional probability.]

= (

=

Correct answer : (1)

24.

A dice is thrown 6 times. If 'getting an even number' is a success, then what is the probability of exactly 5 successes?

a. | $\frac{5}{32}$ | ||

b. | $\frac{3}{32}$ | ||

c. | $\frac{1}{16}$ | ||

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

=

Probability of failure,

= 1 -

P(

[Binomial distribution.]

P(exactly 5 successes) =

=

Correct answer : (2)

25.

A coin is tossed 5 times. If 'getting a head' is considered as a success, find the probability of at least 3 successes.

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

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

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

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

Probability of failure,

P(

[Binomial distribution.]

P(

=

=

=

Correct answer : (2)

26.

A box contains 20 cards labeled 1 through 20. One card is drawn from it at random. What is the probability of getting an odd number and the odds in favor of getting an odd number?

a. | $\frac{2}{5}$ and 1 : 1 | ||

b. | $\frac{1}{10}$ and 1 : 2 | ||

c. | $\frac{9}{10}$ and 1 : 2 | ||

d. | $\frac{1}{2}$ and 1 : 1 |

[There are 10 odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.]

Odds in favor of getting an odd number are 10 : 10 or 1 : 1

[Ten of the outcomes are successes and 10 of them are failures.]

Correct answer : (4)

27.

Fifteen cards labeled A through O are placed in a bag. The bag is shaken and one card is drawn at random. Find the probability of not drawing a vowel.

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

b. | $\frac{4}{5}$ | ||

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

d. | $\frac{11}{15}$ |

[There are 11 ways of not getting a vowel: B, C, D, F, G, H, J, K, L, M, N.]

Correct answer : (4)

28.

If a card is drawn from a bridge deck, what is the probability of getting a king?

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

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

c. | $\frac{1}{52}$ | ||

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

Number of outcomes in E =

=

[

=

Let S be the sample space consists of all cards.

Number of outcomes in S =

=

[

P(E) =

=

Correct answer : (2)

29.

A box contains 20 cards labeled 1 through 20 on them. One card is drawn from it at random. Find the probability of getting an even number.

a. | $\frac{9}{20}$ | ||

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

c. | $\frac{1}{20}$ | ||

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

[There are 10 even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.]

Correct answer : (2)

30.

A box contains 20 cards labeled 1 through 20. One card is drawn from it at random. Find the probability of getting a prime number.

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

b. | $\frac{9}{20}$ | ||

c. | $\frac{1}{5}$ | ||

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

[There are 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19.]

Correct answer : (4)