Question

identify the sample space of the probability experiment and determine the number of outcomes in the sample space. draw a tree diagram. determining a persons letter grade (a, b, c, d, f) and gender (male (m), female (f))
identify the sample space. type your answer.
a. {am, af, aa, bm, bf, ba, cm, cf, ca, dm, df, da}
b. {am, af, bm, bf, cm, cf, dm, df, fm, ff}
c. {am, af, aa, bm, bf, ba, cm, cf, ca}
d. {am, af, bm, bf, cm, cf, dm, df}
there are type your answer. outcomes in the sample space.
choose the correct tree diagram below
oa
ob
oc
od
type your answer.

Explanation:

Step1: Understand sample - space concept

The sample space is the set of all possible outcomes. We have 4 letter - grades (A, B, C, D) and 2 genders (M, F). Each letter - grade can be combined with each gender.

Step2: List all possible combinations

For letter - grade A, we have AM (A and male) and AF (A and female). Similarly for B, we have BM and BF; for C, we have CM and CF; for D, we have DM and DF. So the sample space is {AM, AF, BM, BF, CM, CF, DM, DF}.

Step3: Count number of outcomes

Counting the elements in the sample space {AM, AF, BM, BF, CM, CF, DM, DF}, we find there are 8 outcomes.

Step4: Analyze tree - diagram

The correct tree - diagram should have 4 branches for the letter - grades (A, B, C, D) at the first level, and from each of these branches, 2 sub - branches for male (M) and female (F). Diagram A is the correct one.

Answer:

Identify the sample space: D. {AM, AF, BM, BF, CM, CF, DM, DF}
There are 8 outcomes in the sample space.
Choose the correct tree diagram below: A.