﻿ Probability Worksheets | Problems & Solutions Probability Worksheets

Probability Worksheets
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1.
Find the probability of scoring more than 8 when two dice are rolled.  a. 0.34 b. 0.45 c. 0.62 d. 0.28

Solution:

Number of favorable outcomes = Number of outcomes in which more than 8 can be scored = 10
[The 10 favorable outcomes are (3, 6), (4, 5), (5, 4), (6, 3), (5, 5), (4, 6), (6, 4), (5, 6), (6, 5) and (6, 6).]

Number of possible outcomes = Total number of outcomes when two dice are rolled = 36

P(more than 8) = Number of outcomes with more than 8 scoredTotal number of outcomes

= 1036 = 518 = 0.28
[Substitute and simplify.]

The probability of scoring more than 8 is 0.28.

2.
Are the two events dependent or independent?
1. Drawing a king from a pack of cards without replacing it.
2. Again drawing another king. a. Independent b. Dependent

Solution:

You can draw a king with some probability for the first time.

The number of kings in the pack of cards and the total number of cards is reduced by one, if the previously drawn king is not replaced back.

The probability of drawing a king for the second time is different from the previous draw and is dependent on the previous draw.

The happening of one event is affecting the happening of the other.

So, the two events are dependent.

3.
Are the two events dependent or independent?
1. Tossing a coin.
2. Rolling a dice. a. Independent b. Dependent

Solution:

The two given events are independent events.

This is because, tossing a coin is totally different event from rolling a dice.

The happening of one event is not affecting the happening of the other.

So, the two events are independent.

4.
Nathan rolls a fair die 2 times. Find the probability that he rolls all 6's. a. 0.00277 b. 0.02777 c. 2.777 d. 2.777

Solution:

The probability of getting the number 6 on rolling a fair die = 16

The probability of rolling the number 6 all the 2 times = (1 / 6)2 » 0.02777
[Use multiplication principle of probability.]

5.
Which of the following could not be the probability of an event ? a. 0.96 b. 0.0001 c. $\frac{2}{e}$ d. $\frac{e}{2}$

Solution:

The probability of an event is a real number P, where 0 ≤ P ≤ 1.

Among the choices e2 could not be the probability of an event.
[e2 > 1.]

6.
Ashley has 6 dollars, 4 nickels and 8 dimes in her purse. What is the probability of selecting a dime from her purse? a. 1 b. $\frac{8}{9}$ c. $\frac{1}{18}$ d. $\frac{4}{9}$

Solution:

Number of favorable outcomes = Number of dimes = 8

Number of possible outcomes = Total number of coins = 18

= 49
P(dime) = number of dimestotal number of coins = 8 / 18

Probability of selecting a dime is 4 / 9.

7.
Out of 70 plants, 20 had yellow flowers and 50 had violet flowers. Find the probability of choosing a plant with violet flowers. a. $\frac{1}{7}$ b. $\frac{5}{7}$ c. $\frac{4}{5}$ d. None of the above

Solution:

Number of favorable outcomes = Number of plants with violet flowers = 50

Number of possible outcomes = Total number of plants = 70

P(violet) = Number of favorable outcomesNumber of possible outcomes

= 5070 = 57
[Substitute and simplify.]

The probability of choosing a plant with violet flowers is 5 / 7.

8.
There are 20 paddle boats, 15 boats with oars and 25 motorboats in a boat club. If a boat is chosen at random, what is the probability of not selecting a paddle boat? a. $\frac{2}{3}$ b. $\frac{21}{61}$ c. $\frac{1}{60}$ d. $\frac{3}{11}$

Solution:

Total number of boats = 20 + 15 + 25 = 60

Probability of selecting a paddle boat is 20 out of 60 = 20 / 60 = 1 / 3
[Simplify.]

P(no paddle boat) = 1 - 1 / 3 = 2 / 3
[Substitute and subtract.]

The probability of not selecting a paddle boat is 2 / 3.

9.
A card is drawn from a deck of 52 cards. What is the probability that it is a digit card? a. $\frac{9}{13}$ b. $\frac{9}{11}$ c. $\frac{1}{52}$ d. $\frac{1}{13}$

Solution:

The non-digit cards in the deck of playing cards are a set of ace, jack, king and queen in diamonds, spades, clubs and hearts.

There will be a total of 16 non-digit cards in the deck of playing cards.

Number of digit cards in the deck of cards = Total number of cards in the deck of cards - Number of non-digit cards = 52 - 16 = 36
[Substitute and subtract.]

Number of favorable outcomes = Number of digit cards = 36

Number of possible outcomes = Total number of cards = 52

P(digit card) = Number of digit cardsTotal number of cards = 36 / 52 = 9 / 13
[Substitute and simplify.]

The probability that the card drawn is a digit card is 9 / 13.

10.
A card is drawn from a standard deck of cards. What are the odds in favor of drawing a spade? a. $\frac{1}{39}$ b. $\frac{1}{3}$ c. $\frac{3}{4}$ d. $\frac{1}{12}$

Solution:

Number of favorable outcomes = Number of spades = 13

Number of unfavorable outcomes = Number of cards other than spades = 39
[Since 52 - 13 = 39.]

Odds in favor of an event = Number of favorable outcomesNumber of unfavorable outcomes = 13 / 39 = 1 / 3
[Substitute and simplify.]

Odds in favor of drawing a spade is 1 / 3.