The concept of the probability of the complement pertains to the probability that a certain event will not occur. The calculation involves deducting the probability of the event from the number 1. This method is particularly useful when it's simpler to determine the probability of the event not taking place than the event happening. Understanding this concept is key to grasping the basics of probability theory.
| Topic | Problem | Solution |
|---|---|---|
| None | The television show 50 Minutes has been successfu… | The television show 50 Minutes has been successful for many years. That show recently had a share o… |
| None | A single fair die is tossed. Find the probability… | There are 6 total equally likely outcomes when rolling a fair 6-sided die. |
| None | The table shows the distribution, by age, of a ra… | The total number of moviegoers is 3660. |
| None | The table shows the distribution, by age and gend… | The question is asking for the probability that a randomly selected person in the region is a woman… |
| None | A 12-sided die is rolled. The set of equally like… | A 12-sided die is rolled. The set of equally likely outcomes is \{1,2,3,4,5,6,7,8,9,10,11,12\}. We … |
| None | Use the spinner shown to answer the question. Ass… | Assume that the spinner has n equally sized regions and r of them are red. |
| None | A fair coin is tossed 3 times in succession. The … | The set of equally likely outcomes when a fair coin is tossed 3 times in succession is \(\{\mathrm{… |
| None | Give the probability in decimal form (correct to … | Last year, 1,480 calculators were returned to the manufacturer out of the 84,000 that were produced. |
| None | A standard die is rolled. Find the probability th… | A standard die has 6 faces, numbered 1 through 6. The question asks for the probability that the nu… |
| None | Fourteen of the 100 digital video recorders (DVRs… | Given that there are 14 defective DVRs out of a total of 100 DVRs. |
| None | Among 6245 cases of heart pacemaker malfunctions,… | First, we need to calculate the probability of a single pacemaker not malfunctioning due to firmwar… |
| None | The probability is 0.035 that a male will be colo… | The probability that at least one out of a group of 57 males will be color-blind is equivalent to 1… |
| None | The mean per capita consumption of milk per year … | We are given a problem of probability involving normal distribution. The Central Limit Theorem stat… |
| None | The television show Ghost Whistler has been succe… | The problem is asking for the probability that none of the households are tuned to Ghost Whistler. … |
| None | A manufacturing machine has a 10% defect rate. If… | We are given a manufacturing machine with a 10% defect rate. We are asked to find the probability t… |
| None | Assume that hybridization experiments are conduct… | Given that the probability of a pea having green pods is 0.75 and the peas are selected in groups o… |
| None | 3. For the following problem, the letters of the … | The word 'Mississippi' contains 11 letters. |
| None | Suppose a life insurance company sells a $\$ 240,… | Let's denote the profit that the insurance company makes from selling the policy as a random variab… |
| None | The spinner below shows 5 equally sized slices. R… | Given that Raina spun the dial 1000 times and got the following results: 406 times on white, 384 ti… |
| None | ist The principle of redundancy is used when syst… | The probability that the student's alarm clock will not work on the morning of an important final e… |
| None | In a computer instant messaging survey, responden… | The question is asking for the meaning and value of $P(\bar{D})$. In probability, the bar over a va… |
| None | A research center poll showed that $84 \%$ of peo… | The question is asking for the probability that someone does not believe that it is morally wrong t… |
| None | A modified roulette wheel has 40 slots. One slot … | The question is asking for the probability of getting an even number in a roulette game with 40 slo… |
| None | Of the recent customers at East Coast Dogs, 36 wa… | Let's denote the number of customers who wanted mustard as \(m\) and the number of customers who di… |
| None | 如图所示, 在边长为 1 的正方形 $O A B C$ 中任取一点 $M$, 则点 $M$ 恰好取… | Let's find the area of the shaded region. The shaded region consists of two right triangles and a s… |
| None | Lucy has some number cards that each have a whole… | We are given the probability of choosing an even card as \(\frac{3}{7}\). Let E be the number of ev… |
| None | Q1. For afternoon tea, customer in a café can sel… | Calculate the probability of selecting hot chocolate: \(1 - 0.45 - 0.35 = 0.2\) |
| None | Adam has a bag with 16 green counters, 13 black c… | Find the total number of counters: \(16 + 13 + 21 = 50\) |
| None | A bag with 8 marbles has 4 fed -marbles, 3 bluo f… | 1. Calculate total number of marbles: 4 red + 3 blue + 1 yellow = 8 |
| None | Jason owns a small business selling bagels. He kn… | \(P(\text{credit card})=\frac{\text{number of credit card uses}}{\text{total number of transactions… |
| None | In a popular online role playing game, players ca… | \(Total\ visitors=38+239+12=289\) |