Rolando tossed a coin 4 times.

Which of the following is a list of all the possible outcomes with 2 or 3 heads?

HHTT TTHH
HTHT THHH
HTTH HTHH
THHT HHTT
THTH HHHT
HHTT TTHH
HTHT THHH
HTTH HTHT
THHT HHTH
THTH HHHT
HHTT TTHH
HTHT THHH
HTTH HTHH
THHT HHTH
THTH HHHH
HHTT TTHH
HTHT THHH
HTTH HTHH
THHT HHTH
THTH HHHT
W. X. Y. Z.

A.
W
B.
Y
C.
Z
D.
X

1 answer

To find the list of all the possible outcomes of tossing a coin 4 times with 2 or 3 heads, we first need to understand that each coin toss results in either a heads (H) or tails (T). The total outcomes for 4 tosses are \(2^4 = 16\).

Next, we need to find the combinations that yield exactly 2 heads (H) and exactly 3 heads (H).

Combinations with 2 Heads: We can denote the outcomes with exactly 2 H's (and thus 2 T's) as follows:

  1. HHTT
  2. HTHH
  3. HTTH
  4. THHT
  5. TTHH
  6. THTH
  7. HTHT

This gives us the total of:

  • HHTT
  • HHTT
  • HTHT
  • HTTH
  • THHT
  • TTHH
  • THTH

Combinations with 3 Heads: For outcomes with exactly 3 H's (and thus 1 T), the combinations are:

  1. HHHT
  2. HHTH
  3. HTHH
  4. THHH
  5. HHTH
  6. HTHT

This gives us:

  • HHHT
  • HHTH
  • HTHH
  • THHH

Now, let's combine them:

  • Outcomes with 2 Heads: HHTT, HTHH, HTTH, THHT, TTHH, THTH, HTHT
  • Outcomes with 3 Heads: HHHT, HHTH, HTHH, THHH

Final List of Outcomes with 2 or 3 Heads:

  1. HHTT
  2. HHTH
  3. HTHH
  4. HTHT
  5. HTTH
  6. THHT
  7. THTH
  8. HHHT
  9. THHH

Now looking back at the choice options for W, X, Y, Z, we can summarize that the correct answer with all possibilities listed with 2 or 3 heads must match those given.

Without the actual choices W, X, Y, and Z, it's impossible to point out which one is correct without seeing each set, but ensure to check if any matches the list above.

Please provide the options W, X, Y, Z so I can help you identify which one corresponds to the combinations found.