Exercises: Laplace's rule

A fair die is rolled. Find the probability of each event:

a) Rolling a $3$.

b) Rolling an even number.

c) Rolling a number greater than $4$.

d) Not rolling a $6$.

A ball is drawn at random from the bag shown in the figure, which contains $5$ red balls and $3$ green balls.

Find the probability of:

a) Drawing a red ball.

b) Drawing a green ball.

c) Drawing a yellow ball.

A card is drawn from a Spanish deck of $40$ cards. Find the probability that it is:

a) Coins (Oros).

b) An ace.

c) A face card (jack, knight, or king).

d) The king of cups.

A spinner is divided into $8$ equal sectors numbered from $1$ to $8$. Find the probability that the arrow stops on:

a) $5$.

b) A multiple of $3$.

c) A number greater than $5$.

d) A number less than $9$.

A coin is tossed and a die is rolled. Find the probability of getting:

a) Heads and a $6$.

b) Tails and an odd number.

c) Heads and a number less than $5$.

In a $2.º$ middle school class, there are $14$ girls and $16$ boys. A person is chosen at random to read aloud.

a) What is the probability that it is a girl?

b) And that it is a boy?

Assign a probability to each event and explain why:

a) Rolling a die and getting a number less than $7$.

b) Rolling a die and getting a $8$.

c) Drawing a card from a Spanish deck and getting coins, cups, swords, or clubs.

A tile is chosen at random from a complete set of $28$ dominoes. Find the probability that it is:

a) Double $6$.

b) Any double tile (there are $7$).

c) A tile containing the number $0$ (there are $7$).

The spinner shown in the figure has three sectors with the indicated angles.

Find the probability that the arrow stops on:

a) The red sector.

b) The green sector.

c) A sector that is not yellow.

The letters of the word PROBABILIDAD are written on cards, and one card is drawn at random. Find the probability that it is:

a) A vowel.

b) The letter B.

c) A consonant.

A fair die is rolled. Find the probability of rolling:

a) A multiple of $3$.

b) A prime number.

c) A number less than $7$.

d) A number greater than $6$.

A ball is drawn from a lottery drum containing balls numbered from $1$ to $12$. Find the probability that it is:

a) An even number.

b) A number greater than $8$.

c) A factor of $12$.

d) A multiple of $5$.

a) If the probability of drawing coins in a Spanish deck of cards is $\frac{1}{4}$, what is the probability of not drawing coins?

b) If $P(A) = 0.35$, what is the probability of the complementary event of $A$?

c) An urn contains only red, blue, and green balls. If the probability of drawing a red ball is $\frac{2}{7}$ and that of drawing a blue ball is $\frac{3}{7}$, what is the probability of drawing a green ball?

Two dice are rolled and the sum of the scores is recorded. Use a sample space table to calculate:

a) $P(\text{sum } 7)$

b) $P(\text{sum greater than } 9)$

c) $P(\text{even sum})$

d) $P(\text{sum other than } 7)$

Two coins are tossed. Calculate the probability of getting:

a) Two heads.

b) One head and one tail, in any order.

c) At least one head.

d) No heads.

A card is drawn from a Spanish deck of $40$ cards. Calculate the probability that it is:

a) Coins or a face card.

b) Cups or an ace.

c) Neither a face card nor an ace.

d) Clubs or a number card less than $4$ (the ace counts as $1$).

In a bag there are $5$ red balls, $3$ blue balls and $2$ white balls. A ball is drawn at random. Calculate the probability that:

a) It is not white.

b) It is white or blue.

c) It is yellow.

d) It is not yellow.

The students at a school who do extracurricular sports are distributed as follows:

A student is chosen at random. Calculate the probability that:

a) They are in elementary school.

b) They do swimming.

c) They are in elementary school and play tennis.

d) Given that they are in middle school, they play tennis.

The hour hand of a clock is spun at random. Calculate the probability that it points to a time:

a) Between $3$ o'clock and $4$ o'clock.

b) Before $6$ o'clock.

c) After $10$.

d) Between $2$ and $8$.

A number from $1$ to $50$ is chosen at random. Find the probability that it is:

a) A multiple of $4$.

b) A multiple of $5$.

c) A multiple of $4$ and $5$.

d) A multiple of $4$ or $5$.

The spinner shown in the figure has four sectors with the indicated angles.

Find the probability that the arrow stops on:

a) The red sector.

b) The yellow sector.

c) The blue sector or the green sector.

d) A sector that is not red.

Three coins are tossed. Using a tree diagram, find the probability of getting:

a) Exactly two heads.

b) At least one tail.

c) Three identical outcomes.

d) Exactly one head.

For a Geography exam, students must place the $17$ autonomous communities on an outline map. Ricardo only knows the location of $9$.

a) If he is asked to locate one at random in the exam, what is the probability that it is one of those he knows?

b) If he gets one he does not know and guesses its location among the remaining $8$, what is the probability that he gets it right?

The chart shows the sweets in a bag. One sweet is drawn at random.

Find the probability that it is:

a) Strawberry.

b) Lemon or mint.

c) Not apple.

d) Orange.

To enter a game at the school fair, you must roll a die and get a higher score than the 'guardian', who rolls another die before you.

a) Construct a sample space table with the $36$ possible matchups.

b) What is the probability that you enter the game?

c) What is the probability of tying with the guardian?

d) If the rule were 'score at least twice as many points as the guardian', what would be the probability of entering?

You can do it on paper and send a photo with your answer.

Two dice are rolled and the product of the scores is recorded.

a) Construct the sample space table with the $36$ products.

b) Calculate the probability that the product is even.

c) Calculate the probability that the product is a multiple of $5$.

d) Calculate the probability that the product is greater than $20$.

You can do it on paper and send a photo with your answer.

In an urn there are $4$ red balls and $6$ green balls. How many blue balls must be added so that the probability of drawing a red ball is $\frac{1}{4}$? Set up the equation and solve it.

In a class of $30$ students there are $18$ girls, of whom $12$ have passed all subjects. In total, $10$ students in the class have failed at least one subject.

a) Construct a two-way table (girls/boys versus passed everything/failed at least one subject).

b) If a person is chosen at random, what is the probability that they are a boy and have passed everything?

c) Given that the chosen person has failed at least one subject, what is the probability that she is a girl?

You can do it on paper and send a photo with your answer.

In a family with two children, Nerea reasons: 'There are three possible outcomes: two boys, two girls, or one of each; therefore, the probability that both are boys is $\frac{1}{3}$.'

a) Explain why her reasoning is incorrect.

b) Write down the correct sample space, taking birth order into account, and calculate the correct probability.

c) What is the probability that there is at least one girl?

A tetrahedral die has its faces numbered $1$, $2$, $2$ and $3$, and another tetrahedral die has $2$, $3$, $3$ and $4$. Both are rolled and the product is recorded.

a) Construct the sample space table with the $16$ possible products.

b) Calculate the probability that the product is even.

c) Calculate the probability that the product is $6$.

You can do it on paper and send a photo with your answer.

An NGO sells $200$ raffle tickets numbered from $000$ to $199$ for a charity draw. One ticket is drawn at random. Calculate the probability that the winning number:

a) Contains the digit $7$.

b) Is a multiple of $10$.

c) Starts with the digit $1$.

d) Has all three digits equal.

Two cards are drawn from a standard Spanish deck of $40$ cards, without replacing the first card in the deck.

a) What is the probability that the first card is coins?

b) If the first card was coins, what is the probability that the second card is also coins?

c) What is the probability that both cards are coins?

d) And what is the probability that neither card is coins?