Question

There are 5 Snickers, 10 Baby Ruths, 13 Milky Ways, 12 Twix’s’ and 17 Almond Joys in a bowl of candy. You reach into the bowl and randomly select 5 candy bars. Use this information to answer the following two questions.

1.       What is the probability that you select exactly 2 Milky Way bars?

2.       What is the probability that you select 3 or fewer Almond Joys?

Hints:

a) Determine what kind of probability density function this is. Cite 2 reasons for your choice.

b) Formulate the 2 questions above in probability terms; P(x)

c) Using the appropriate Excel function, make a table showing its five arguments for each question.

d) Use the Excel function to solve problems 1 and 2

Answer 1

total items = 5 + 10 + 13 + 12 + 17 =57

total milky ways= 13

it is hyper geometric distribution and probability given by

P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)

where,

Sample size,     n =    5
No. of events of interest in population    , k =   13
Population size   , N =   57
success from sample ,   x =    2

1)

P(exactly 2 milky ways) = P(X=2 ) = 13C2 * (57-13)C3 / 57C5 = 0.24672

excel function:   =HYPGEOMDIST(2,5,13,57)

2)

number of almond joys=17

P(3 or fewer almond joys) = P(X≤3) = 0.9758

excel function: =HYPGEOM.DIST(3,5,17,57,TRUE)