Question

Part 1: Seventeen items are found in a box, eight of which are observed to exhibit a particularly desirable property. Suppose six of these items are randomly selected from the box without replacement and let X be the random variable representing the number among the six that exhibit the desirable property.

Compute (round answer to four decimal places) P(X = 4) =

Part 2 : The probability of observing a certain event is 0.4. Suppose we make repeated observations until we have observed the desired event two times.What is the probability that we make four observations in order to have observed the desired event two times.? (Round your answer to four decimal places

Answer 1

the box particular of which desirable. There are 17 items in 8 items exhibit a property. pl an item to exhibit property) desirable 17 Let X be the random variable denoting the number among the & which exhibit the desirable property. xn Binomial (n=6, p = 8). » P(x = 4) = ( ) ( ) ( 18 ) 2 15 (9)' (7) - 0.206178 178 2 0.2062 (opto 4 de cimal. places). Now Plobserving a certain event) = 0.4. Let y be the rando en variable de noting getting the total nomber of times we get desired event out of 4 times. yn Binomial (4, 0:4).

P(Y=2 ) = (4) (0.4² (1-0.42 6 (0.4) (06) ² - 0.3456