In probability theory, outcomes are the results of random experiments, while events are collections of outcomes. For example, in the experiment of tossing a coin, the outcomes are 'Head' and 'Tail', and each is regarded as an event. In throwing a die, outcomes include numbers 1 to 6, and events can include getting an even number (events 2, 4, 6). The probability of an event can be calculated by taking the ratio of the number of favorable outcomes that constitute the event over the total number of equally likely outcomes from the experiment. For example, if a bag contains 4 red balls and 2 yellow balls, the probability of drawing a red ball is defined by the favorable outcomes (4) over total outcomes (6). This systematic approach to understanding events and outcomes is crucial in predicting and interpreting results in probabilistic terms.
Similar Questions
1.A bag has 5 green balls and 3 black balls. (The balls are identical in all respects other than color.) A ball is drawn from the bag without looking into the bag. What is the probability of getting a green ball? Is it more or less than getting a black ball?
Solution: There are in all \(5 + 3 = 8\) outcomes of the event. Getting a green ball consists of 5 outcomes. Therefore, the probability of getting a green ball is \( \frac{5}{8} \). In the same way, the probability of getting a black ball is \( \frac{3}{8} \). Therefore, the probability of getting a green ball is more than that of getting a black ball.
2.A jar contains 4 blue marbles and 6 red marbles. (The marbles are identical in all respects other than color.) A marble is picked from the jar without looking. What is the chance of picking a red marble? Is this chance greater or smaller than that of picking a blue marble?
Solution: There are in all \(4 + 6 = 10\) outcomes of the event. Picking a red marble has 6 outcomes. Therefore, the probability of picking a red marble is \( \frac{6}{10} = \frac{3}{5} \). Similarly, the probability of picking a blue marble is \( \frac{4}{10} = \frac{2}{5} \). Thus, the probability of picking a red marble is greater than that of picking a blue marble.
3.A box contains 8 orange candies and 2 lemon candies. (The candies are identical in all respects other than flavor.) If a candy is chosen from the box without looking, what is the probability of selecting an orange candy? Is this probability more than that of selecting a lemon candy?
Solution: There are in all \(8 + 2 = 10\) outcomes of the event. Selecting an orange candy consists of 8 outcomes. Therefore, the probability of selecting an orange candy is \( \frac{8}{10} = \frac{4}{5} \). In the same manner, the probability of selecting a lemon candy is \( \frac{2}{10} = \frac{1}{5} \). Thus, the probability of selecting an orange candy is more than that of selecting a lemon candy.
4.A crate holds 3 white balls and 7 black balls. (The balls are identical in all respects except color.) If a ball is drawn from the crate without peeking, what’s the probability of getting a white ball? Is it higher or lower than that of getting a black ball?
Solution: There are in total \(3 + 7 = 10\) outcomes of the event. Getting a white ball consists of 3 outcomes. Therefore, the probability of getting a white ball is \( \frac{3}{10} \). Likewise, the probability of getting a black ball is \( \frac{7}{10} \). Hence, the probability of getting a white ball is lower than that of getting a black ball.