Rocket Launch Day: Map the Outcomes

Organize compound outcomes and identify the outcomes in an event.

Lists and Tables

Each task describes a separate launch-day experiment. A sample space contains every possible outcome. Read codes in the stated order.

A team randomly chooses a nose shape: cone (C) or dome (D). Then it randomly chooses a recovery system: parachute (P) or streamer (S). Each outcome lists nose shape first. Which list is the complete sample space?

A. {CP, CS, DP, DS}B. {C, D, P, S}C. {CP, PC, DS, SD}D. {CP, CS, DP}

Use the nose and recovery choices from Question 1. Select every outcome in the event “the rocket has a dome nose or a streamer, or both.”

A camera trial randomly chooses a launch pad (1, 2, or 3) and a view: ground (G) or aerial (A). Every pad can use either view. Each code lists the pad first.

Camera Trial Sample Space
Pad	Ground view	Aerial view
1	1G	1A
2	2G	?
3	?	3A

Complete the table. Write the code for pad 2 with an aerial view: . Write the code for pad 3 with a ground view: .

Use the camera trial in Question 3. The event is “an aerial view from a pad numbered greater than 1.”

How many outcomes belong to this event? outcomes

For a display rocket, a team randomly chooses a body color: red (R) or violet (V), then a fin count: 3, 4, or 5. Any color can have any fin count. Which organized list contains every possible outcome exactly once?

A. {R3, V4, R5, V3, R4, R5}B. {R3, R4, R5, V3, V4, V5}C. {R3, R4, V4, V5}D. {R3, R4, R5, V3, V4}

Tree Paths

Follow one branch at each stage. Each complete path represents one outcome. The trees show possible choices, not probabilities.

For Questions 6–7, a launch simulation records wind first: light (L) or moderate (M). It then records camera status: on (Y) or off (N). Finally, it records recovery: parachute (P) or streamer (S). All combinations are possible.
Start
├─ L
│ ├─ Y → P or S
│ └─ N → P or S
└─ M
├─ Y → P or S
└─ N → P or S

How many complete paths are in the simulation tree? paths

Select every outcome in the event “the camera is on and the recovery system is a streamer.” Codes follow the order wind–camera–recovery.

Two launches are scheduled. Each launch can proceed (P) or be delayed (D), regardless of the other launch. Draw a tree diagram showing the first launch and then the second launch. Label every branch and write the two-letter outcome at the end of every complete path.

A payload trial chooses a sensor first: temperature (T) or pressure (P). The next choice is a recording interval. Temperature can use 1, 2, or 5 seconds. Pressure can use only 2 or 5 seconds. The tree summarizes these choices.
Start
├─ T → 1, 2, or 5
└─ P → 2 or 5
Which list gives the complete sample space?

A. {T1, T2, T5, P2, P5}B. {T1, P2, P5}C. {T1, T2, T5, P1, P2, P5}D. {T1, T2, P2, P5}

10.

A photo team randomly chooses a camera position: east (E) or west (W), then a lens: wide (A) or zoom (Z), then a photo mode: single (S) or burst (B). Every combination is possible. The event is “burst mode with either an east position or a zoom lens, or both.”

Complete an organized list of the event's outcomes. Write the missing three-letter code, using position–lens–mode order: {EAB, EZB, }.

Order and Restrictions

Check whether a choice can repeat and whether changing the order creates a different outcome.

11.

Cards labeled 1, 2, and 3 represent three launch pads. A coordinator draws one card, keeps it out, and draws a second card. The code records the first draw followed by the second draw. Which list is the complete sample space?

A. {11, 12, 13, 21, 22, 23, 31, 32, 33}B. {12, 13, 23}C. {11, 22, 33}D. {12, 13, 21, 23, 31, 32}

12.

Use the two-card experiment in Question 11. Select every outcome in the event “the second pad number is greater than the first pad number.”

13.

Three rockets are named Ember (E), Nova (N), and Pulse (P). A coordinator chooses two different rockets in launch order, then chooses a morning (M) or afternoon (A) session. Each code lists first rocket–second rocket–session. Which list contains all outcomes in the event “Nova launches first in the afternoon”?

A. {NEA, NPA, ENA, PNA}B. {NEM, NPM}C. {NEA, NPA}D. {NEA, NPA, NNA}

14.

For two practice countdowns, a team randomly chooses a short (S) or long (L) countdown each time. Either choice may repeat. The first and second countdowns are recorded in order. Ari lists the sample space as {SS, SL, LL}, saying, “SL and LS use the same choices, so we only need one.” Explain the error. Write the complete sample space and identify all outcomes with exactly one long countdown.