An experiment consists of two independent trials. the outcomes of the first trial are a, b, and c, with probabilities of occurring equal to 0.3, 0.2, and 0.5, respectively. the outcomes of the second trial are e and f, with probabilities of occurring equal to 0.3 and 0.7. draw a tree diagram representing this experiment. use this tree diagram to find the probabilities below.
(a) p(b)
(b) p(f | b)
(c) p(b intersection f)
(d) p(f)

Asphere has a diameter of 10 in. what is the volume of the sphere?

Anita has a success rate of 80% on free throws in basketball. she wants to know the estimated probability that she can make exactly four of five free throws in her next game. how can she simulate this scenario? categorize each simulation of this scenario as correct or incorrect.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.