A company always sends letters by second class post unless they are marked first class. Over a long period of time it has been established that 45 per cent of letters to be posted are marked first class. In a random selection of 10 letters to be posted, find the probability that the number marked first class is (a) at least 3, (b) fewer than 2. One Monday morning there are only 32 first class stamps. Given that there are 80 letters to be posted that day, (c) use a suitable approximation to find the probability that there are enough first-class stamps.

2. If there are 5 pieces of gum and 3 candies in a box and 3 of them are taken at random, generate the probability distribution for the number of candies that came out in the sample.

American Airlines' flights from Chicago to Dallas are on time 70 % of the time. Suppose 13 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 2 flights are on time is = 2.The probability that at most 4 flights are on time is = 3.The probability that exactly 6 flights are on time is =

Assume that when adults with smartphones are randomly​ selected, 43% use them in meetings or classes. If 14 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes. The probability is?

Assume for this problem that the company has 8 BMWs and 5 Hondas, and two cars are selected randomly and given to sales representatives. What is the probability of both cars being BMWs, given that both are of the same make?

According to an​ airline, flights on a certain route are on time 75​% of the time. Suppose 25 flights are randomly selected and the number of​ on-time flights is recorded. N=25 P=0.75 ​(c) Find and interpret the probability that exactly 14 flights are on time. ​(d) Find and interpret the probability that fewer than 14 flights are on time. ​(e) Find and interpret the probability that at least 14 flights are on time. ​(f) Find and interpret the probability that between 12 and 14 flights, inclusive, are on time.   (c) The probability that exactly 14 flights are on time is ____?  ​(Round to four decimal places as​ needed.) Interpret the probability. In 100 trials of this​ experiment, it is expected that about ____ will result in exactly 14 flights being on time. (Round to nearest whole number as needed) (d) The probability that fewer than 14 flights are on time is ____? (Round to four decimal places as​ needed.) Interpret the probability. In 100 trials of this​ experiment, it is expected…

10% are born as left handed. Calculate the probability that in a batch of 150 students, there are most 10 of them are left handed

A poll is given, showing 60% are in favor of a new building project.If 6 people are chosen at random, what is the probability that exactly 2 of them favor the new building project?

Delta Airlines' flights from Boston to Dallas are on time 60 % of the time. Suppose 13 flights are randomly selected, and the number on-time flights is recorded.1.The probability that at least 9 flights are on time is =2.The probability that at most 8 flights are on time is =3.The probability that exactly 12 flights are on time is =

Suppose a math class contains 41 students, 19 females (two of whom speak French) and 22 males (three of whom speak French). Compute the probability that a randomly selected student is male, given that the student speaks French.