The sample space of an experiment is S= {1,2,3}. Each outcome is equally likely to occur with a probability of 1/3. What is the probability of picking number 2 or 3? Write your answer in simplest form as a fraction.
There are two outcomes in the sample space that satisfy the event of picking number 2 or 3, namely 2 and 3. The sum of probabilities of these outcomes is:
P(2 or 3) = P(2) + P(3) = 1/3 + 1/3 = 2/3
Therefore, the probability of picking number 2 or 3 is 2/3.
Mr. Lim has a bag with some marbles colored red, yellow, green, blue, and white. The marbles are identical in number. If there are 40 marbles in the bag, how many marbles of each color are in the bag?
If there are five different colors of marbles, and each color has the same number of marbles, then we can represent the number of marbles of each color as x. Therefore, the total number of marbles is:
x + x + x + x + x = 5x
We also know that there are 40 marbles in the bag, so:
5x = 40
Solving for x, we get:
x = 8
Therefore, there are 8 marbles of each color in the bag.
Mr. Lim has a bag with some marbles colored red, yellow, green, blue, and white. The marbles are identical and number. Mr. Lim will conduct a chance experiment by randomly drawing a marble from the bag and then returning it after noting the color. Based on 50 trials, how many green marbles for Mr. limit expect to pick?
If each marble is identical and the experiment involves randomly drawing a marble from the bag and returning it, then we can assume that each draw has the same probability of picking a green marble. Let p be the probability of picking a green marble, then:
p = (number of green marbles) / (total number of marbles)
Since all marbles are identical, we can represent the probability p as:
p = 1 / 5
Therefore, the expected number of green marbles that Mr. Lim will pick in 50 trials is:
E(green marbles) = (total number of trials) x (probability of picking a green marble) = 50 x (1/5) = 10
So, Mr. Lim can expect to pick 10 green marbles in 50 trials. However, it's important to note that the actual number of green marbles picked may vary from this expected value due to chance variability.
Company X tested its lightbulbs to see how long they would last. On a production line, 2500 bulbs were taken and tested. The department in charge reported that out of 2500 bulbs, there are 2200 bulbs that burnt out more than 1500 hours of use. Lucy purchased a lightbulb from company X. What is the likelihood that it will burn for more than 1500 hours? Write your answer in decimal form.
The proportion of bulbs that burnt out more than 1500 hours of use in the sample of 2500 bulbs is:
2200/2500 = 0.88
This is the estimated probability that a lightbulb from company X will burn for more than 1500 hours. Therefore, the likelihood that Lucy's lightbulb will burn for more than 1500 hours is 0.88, or 88% (in decimal form).