Kim, Maria, Ian, Jim, Sergio, and Simone have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. A in how many ways can they arrive? B. In how many ways can kim arrive first and simone last?

C. Find the probability that kim will arrive first and simone last.

Step-by-step explanation:

A. The order matters, so use permutations.  The number of ways that 6 people can be arranged is:

₆P₆ = 6! = 720

B. If Kim is first, and Simone is last, then the number of ways the remaining 4 people can be arranged is:

₄P₄ = 4! = 24

C. Of the 720 total arrangements, there are 24 in which Kim is first and Simone is last.  So the probability is 24/720 = 1/30.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.