There are 5 red pens,3 blue pens and 2 green pens in a box. gary takes at random a pen from the box and gives the pen to his friend. gary then takes at random another pen from the box . work out the probability that both pens are the same colour.

Jasmine wants to eat at 8: 00pm her meal takes 65mins to cook what time does she need to put the meal in the oven

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Mikes car gets an average of 28 mpg. there are 12 gallons of fuel in mikes car when he starts his trip of 140 miles. about how many gallons are left at the end of his trip?