The likelihood of events that are not mutually exclusive is determined by adding the probabilities of each event and then subtracting the probability of them happening together. These events have the potential to occur at the same time, which sets them apart from mutually exclusive events. Grasping this concept is vital when delving into the realms of probability theory and statistical analysis.
| Topic | Problem | Solution |
|---|---|---|
| None | You are dealt one card from a 52-card deck. Find … | We are given a standard 52-card deck and we are to find the probability of drawing a five or a blac… |
| None | The table shows the number, expressed in millions… | First, we need to calculate the total number of people who moved in 2004. This is done by adding up… |
| None | Of the 35 plays attributed to a playwright, 13 ar… | Define the total number of plays, which is 35. |
| None | One card is randomly selected from a deck of card… | The deck of cards has 52 cards in total, with 13 cards of each suit (hearts, diamonds, clubs, spade… |
| None | It is equally probable that the pointer on the sp… | The problem is asking for the probability that the pointer will stop on an odd number or a number g… |
| None | If you are dealt 3 cards from a shuffled deck of … | We are given a shuffled deck of 52 cards and we are to find the probability of getting one queen an… |
| None | If you are dealt 4 cards from a shuffled deck of … | The picture cards in a deck are the Kings, Queens, and Jacks. There are 4 of each in a deck, so the… |
| None | You select a family with four children. If $\math… | Define the set of equally likely outcomes for the children's genders as [FFFF, FFFM, FFMF, FMFF, MF… |
| None | Suppose that $45 \%$ of all babies born in a part… | We are given that 45% of all babies born in a particular hospital are boys. If 7 babies born in the… |
| None | In the game of blackjack played with one deck, a … | In the game of blackjack played with one deck, a player is initially dealt 2 different cards from t… |
| None | In a recent year, about $35 \%$ of all infants bo… | Given that 35% of all infants born in a country were conceived through in-vitro fertilization (IVF)… |
| None | Two cards are selected from a standard deck of 52… | Define the total number of cards in a deck, which is 52, and the number of eights and sevens in the… |
| None | Of the cartons produced by a company, $9 \%$ have… | Given that the probability of a carton having a puncture is 9%, the probability of a carton having … |
| None | A physics class has 40 students. Of these, 11 stu… | Given that there are 40 students in a physics class, 13 of which are female and 11 are physics majo… |
| None | The data on the right represent the number of liv… | First, we need to calculate the total number of multiple births. This is done by adding up all the … |
| None | There are 8 black balls and 8 red balls in an urn… | We are given that there are 8 black balls and 8 red balls in an urn. We are asked to find the proba… |
| None | Most railroad cars are owned by individual railro… | We can model the situation as a Markov Chain with two states: 'Home' and 'Pool'. Each month, 7% of … |
| None | If a salesperson has gross sales of over $\$ 600,… | To win a $27,000 bonus, the salesperson must draw all the bills before drawing the twenty-dollar bi… |
| None | The table below shows the results of a survey tha… | Given the total number of people surveyed is 2861, the total number of males is 1479, the total num… |
| None | 15 students were asked to choose between the broa… | Given data of 15 students with their gender and preference of study. |
| None | If you are dealt 7 cards from a shuffled deck of … | The total number of ways to draw 7 cards from a deck of 52 is given by the combination formula \(C(… |
| None | A presidential candidate plans to begin her campa… | A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 41 states. We… |
| None | You are certain to get 2 kings when selecting 50 … | First, we need to calculate the total number of ways to select 50 cards from a deck of 52 cards. Th… |
| None | There are 3 children in each of 3 different famil… | Let's find the total number of ways to choose 2 children from all the families. There are 9 childre… |
| None | At LaGuardia Airport for a certain nightly flight… | Given probabilities: \(P(rain) = 0.06\), \(P(delay) = 0.09\), \(P(not\ rain\ and\ on\ time) = 0.86\) |
| None | Consider a standard deck of 52 cards, with four s… | Find the probability of drawing an Ace: \(P(A) = \frac{4}{52}\) |
| None | In a certain Algebra 2 class of 24 students, 6 of… | Let x be the number of students who play both sports. Then, we have the equation: \(6 + 16 - x = 18… |
| None | 29. (a) In this part you may use this Venn diagra… | \(n(F \cap S) = n(F) + n(S) - n(F \cup S)\) |