Probability

A survey showed that 45 out of 150 people prefer tea over coffee. What is the relative frequency of people who prefer tea?

A student has 10 shirts: 3 white, 2 blue, and 5 grey. What is the probability of the student choosing a white shirt at random?

A spinner has 4 equal sections: 1, 2, 3, and 4. If spun once, what is the probability of getting a number less than 4?

If $P(E) = 0.05$, what is $P(\text{not } E)$?

A biased coin is flipped 60 times and lands on heads 45 times. If it is flipped another 100 times, how many more heads would you expect?

In a school of 200 students, 120 play sports. Of those who play sports, 40 also play a musical instrument. If 30 students play an instrument but not sports, how many students do neither?

A bag contains 3 red, 4 white, and 5 blue balls. If two balls are drawn with replacement, what is the probability that at least one is red?

A bag contains 10 coins. 9 are fair and 1 is double-headed. A coin is chosen at random and tossed 5 times. If it shows heads every time, what is the probability it is the double-headed coin?

A random variable $X$ can take values 1, 2, or 3 with probabilities $P(1) = m, P(2) = m^2, P(3) = m$. Find the value of $m$.

Three points are chosen at random on the circumference of a circle. What is the probability that they lie on a semicircle?

Events $A, B$, and $C$ are mutually exclusive. $P(A) = 0.2, P(B) = 0.3, P(C) = 0.4$. What is the probability that $A, B$, or $C$ occurs?

A bag contains 2 red and 3 blue chips. A chip is drawn, replaced, and another is drawn. What is the probability that both are red?

A coin is tossed twice. What is the probability of getting at least one 'Head'?

Events $A$ and $B$ are independent. $P(A) = 0.5$ and $P(B) = 0.4$. What is the probability that both $A$ and $B$ occur?

Given $P(A') = 0.7, P(B') = 0.8,$ and $P(A \cap B) = 0.1$. Find $P(A \cup B)$.

Two fair dice are rolled. What is the probability that neither die shows a 6?

Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that one card is a King and the other is a Queen?

In a group, 70% like tea, 60% like coffee, and 20% like neither. If a person is chosen at random, what is the probability they like both tea and coffee?

A bag contains 3 red and 7 blue balls. Two balls are drawn. Find the difference between the probability of drawing two red balls with replacement and without replacement.

If $A \subset B$, and $P(A) = 0.3, P(B) = 0.7$, what is $P(A|B)$?

A tree diagram shows $P(\text{Win}) = 0.7$. If two matches are played, what is the probability of winning the first match and losing the second?

A box contains $6$ blue and $4$ pink ribbons. A ribbon is selected and replaced. What is the probability of selecting a pink ribbon then another pink ribbon?

If you flip a coin ($P(H)=0.5$) and then roll a die ($P(6)=1/6$), what is the probability of getting a Head and then a 6?

A tree diagram has 3 branches at the first stage: A, B, and C. If $P(A)=0.1$ and $P(B)=0.6$, what is $P(C)$?

A container holds $5$ purple and $5$ white marbles. Two marbles are selected without replacement. What is the probability that both are the same color?

The probability that an email is spam is $0.7$. A filter correctly identifies spam $95\%$ of the time. However, it also incorrectly filters non-spam emails as spam $1\%$ of the time. What is the probability that an email is not filtered out?

A purse contains $4$ gold coins and $6$ silver coins. A coin is picked, replaced, and then a second coin is picked. What is the probability that both coins are gold?

A bag contains $6$ red and $4$ blue tokens. One token is drawn and its color noted. It is NOT replaced. A second token is drawn. If the first was red, $2$ more red tokens are added to the bag before the second draw. If the first was blue, $2$ more blue tokens are added. Find the probability the second token is blue.

A box contains $x$ red balls and $5$ blue balls. Two balls are drawn without replacement. The probability that both are blue is $\frac{2}{9}$. Find $x$.

A game is played by rolling a die. If you roll a 6, you win. If you don't, you roll again. You have a maximum of 3 rolls. What is the probability you win?

If $P(A) = 0.9$ and $P(B|A) = 0.1$, what is $P(A \cap B)$?

A group of 40 people were asked if they like apples or oranges. 25 like apples, 20 like oranges, and 10 like both. If a person who likes oranges is chosen, what is the probability they also like apples?

The probability that it rains is 0.3. The probability that it rains and I use an umbrella is 0.24. If it rains, what is the probability I use an umbrella?

There are 20 chocolates in a box: 12 are milk chocolate and 8 are dark chocolate. If you eat one milk chocolate, what is the probability the next one you pick at random is dark chocolate?

A box contains 12 light bulbs, 4 of which are defective. If two bulbs are chosen without replacement, what is the probability that the second bulb is defective given that the first bulb was good?

Given $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cap B) = 0.1$, find $P(A|B')$.

A bag contains 5 red and 5 blue marbles. Three marbles are drawn without replacement. What is the probability that the third marble is red, given that the first two were red?

A box has 2 red, 3 green, and 4 blue balls. Three balls are drawn without replacement. Given that the first ball is red and the second ball is green, what is the probability that the third ball is blue?

Two integers $x$ and $y$ are chosen from the set $\{1, 2, 3, 4, 5\}$ without replacement. Given that $x+y$ is even, what is the probability that $x$ is odd?

In a game of bridge, a player is dealt 13 cards from a 52-card deck. Given that the player has at least one Ace, what is the probability they have at least two Aces?