Question

Dave, Frida, Natalie, and Robbie have four adjacent seats at a baseball park. They randomly chose an order to sit in. Make a list of all the possible ways in which they can sit in the four seats. Then match the events to their correct probabilities.
1/2 or 1/3 or 1/6 chance?


the probability of Dave and
Natalie sitting together

the probability of sitting
boy, girl, boy, girl or
girl, boy, girl, boy

the probability of the two
boys sitting in the middle

the probability of Frida and
Natalie sitting together

the probability of Robbie
sitting between the girls

the probability of Natalie
sitting between Dave and Robbie

Answer 1

The sample space (list of outcomes) is:
DFNR; DFRN; DRFN; DRNF; DNFR; DNRF;
NFDR; NFRD; NRFD; NRDF; NDRF; NDFR;
RFDN; RFND; RNFD; RNDF; RDFN; RDNF;
FRDN; FRND; FNRD; FNDR; FDRN; FDNR

P(Dave beside Natalie) = 1/2
P(B,G,B,G or G,B,G,B) = 1/3
P(boys in the middle) = 1/6
P(Frida beside Natalie) = 1/2
P(Robbie between Frida & Natalie) = 1/6
P(Natalie between Dave & Robbie) = 1/6

Explanation
Letting D=Dave, R=Robbie, N=Natalie, and F=Frida you get the list of possibilites above.

For P(Dave beside Natalie), look for DN or ND.  This appears 12 times out of the 24 possibilities above; 12/24 = 1/2.

For P(B,G,B,G or G,B,G,B), we have the possibilities DFRN, DNRF, RFDN, RNDF, FRND, FDNR, NDFR, NRFD.  There are 8 possibilites out of 24; 8/24 = 1/3.

For P(Frida beside Natalie), look for NF or FN.  This appears 12 times out of the 24 possibilities; 12/24 = 1/2.

For Robbie between Frida and Natalie, look for FRN or NRF.  This appears 4 times out of 24; 4/24 = 1/6.

For Natalie between Robbie and Dave, look for RND or DNR.  This appears 4 times out of 24; 4/24 = 1/6.