Search & Filtering
Confidence level=97%
Two dice are thrown. What is the probability that the first die rolls a 1 if it is known that the number of points on the second die is higher than on the first?
From a pocket containing 10 coins (20 cents each) and 10 coins (3 cents each), 10 coins are taken randomly. What is the probability that the amount of money left in the pocket is not less than the one taken out
The multiple-choice question on a combinatorics quiz contains 20 questions with ten possible answers each (where only 1 answer is true). Compute the probability of randomly guessing the correct answers and getting at least 10 correct answers to 20 questions (Event A). Find the mathematical expectation and variance of the number of correct answers.
Two boxes, 1 and 2 are given. Suppose box 1 contains 6 black and 7 white balls. Box 2 contains 9 black and 8 white balls. Three balls are selected at random from box 1 and put into box 2. Then two balls are selected at random from box 2.
1) what is the probability that these two balls have the same color
2) what is the probability that these two balls have the different colors
An elevator starts with 4 passengers and stops at 4 floors. Find the probability of the following events:
1) all passengers leave at the same floor (Event A)
2) all passengers leave at the two floors (Event B)
3) all passengers leave at the three floors (Event C)
4) all passengers leave at different floors (Event D)
A Biotech company produces enzymes at a rate that can be described by the Poisson process.
Their lipase enzyme from a genetically modified bacteria produces glycerol at an average rate of
3 mg/L per minute.
4.1 Find the probability that the enzyme will produce exactly 5 mg/L in a given minute. (2)
4.2 What is the likelihood that the enzyme will produce four or more mg/L in a given minute? (7)
4.3 What chance is there that no product will be produced in a given minute?
The manager of a local gym has determined that the length of time patrons spend at the gym is a
normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.
5.1 What proportion of patrons spends more than 2 hours at the gym? (3)
5.2 What proportion of patrons spend less than 1 hour at the gym? (3)
5.3 What is the least amount of time spent by 60% of patrons at the gym?
Calculate the average price paid per kilogram of sodium hydroxide in a lab storeroom consisting
of 40 kilograms bought for R15 each; 10 kilograms bought for R20 each; 5 kilograms bought for
R40 each; and 50 kilograms bought for R10 each.
The heights of male are normally distributed with mean of 170 cm and standard deviation of 7.5cm. Find the probability that a randomly selected male has a height > 180 cm.
