The conditional probability in relation to independent events can be described as the likelihood of a specific event happening after another event has already taken place. For events that are independent, the conditional probability is merely the probability of the event itself, due to the fact that the occurrence of the previous event has no influence on it.
| Topic | Problem | Solution |
|---|---|---|
| None | You are to randomly pick one disk from a bag that… | The problem is asking for the probability of picking a disk that is yellow, given that the disk has… |
| None | Suppose you have 3 jars with the following conten… | First, we need to calculate the probability of drawing a white ball from each jar. For Jar 1, there… |
| None | The numbered disks shown are placed in a box and … | The problem is asking for the conditional probability of selecting an even number given that a gree… |
| None | Elizabeth brought a box of donuts to share. There… | Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identic… |
| None | A marble jar contains a total of 164 marbles. The… | The problem involves a jar of 164 marbles with different colors. The frequency of each color is as … |
| None | A single card is drawn from a standard deck of ca… | The problem is asking for the conditional probability of drawing a queen given that the card drawn … |
| None | Suppose there is a $11.9 \%$ probability that a r… | We are given two probabilities: |
| None | From the sample space $S=\{1,2,3,4, \ldots, 15\}$… | From the sample space $S=\{1,2,3,4, \ldots, 15\}$ a single number is to be selected at random. Give… |
| None | Every year, $10 \%$ of the population of San Fran… | The problem is asking for the probability that a person currently living in Sacramento will be livi… |
| None | Given that a person's last cola purchase was Coke… | This problem can be modeled as a Markov Chain with two states: Coke and Pepsi. The transition proba… |
| None | Five hundred consumers are surveyed about a new b… | Find the probabilities P(A and B) and P(B) from the given table: |
| None | Un bocal contient 7 bonbons bleus, 3 jaunes et 10… | Calculer la probabilité de tirer un bonbon bleu : \(\frac{7}{20}\) soit \(0.35\) |
| None | This season, the probability that the Yankees wil… | Given probabilities: P(Yankees win) = 0.51, P(Yankees score 5 or more runs) = 0.49, P(Yankees win a… |
| None | A bag contains red and green chips. Some of the c… | We are given $P(G) = 0.4$, $P(S) = 0.5$, and $P(G \text{ and } S) = 0.3$. We need to find $P(S \mid… |
| None | - Of the cars on a used car lot, $70 \%$ have air… | Given probabilities: P(AC) = 0.7, P(CD) = 0.4, P(CD ∩ AC) = 0.2 |
| None | 4. michael has a jar containing is dimes and 20 q… | Let A be the event that first coin is a dime, B be the event that second coin is different from the… |