"What are the odds?" That There is a Doctor on My Flight

"I am serious. And don't call me Shirley." Unless you have someone like Leslie Nielsen on board, the question "is there a doctor on the plane?" isn't one you generally want to hear. Apparently, airlines don't really want the answer to be yes. But what are the chances that there is a doctor on board your flight, should there be a medical emergency in the air?

The answer entirely comes down to the size of the plane you're flying on, assuming that doctors on airplanes show up as frequently as they do in the general population in the U.S. (295 per 100,000 people). The larger the plane, the more likely it is that at least one of the other passengers is a physician.

I assumed that you're not traveling alone, but with 1 other person (and they are not a doctor). That leaves n - 2 other people to draw a doctor from, where n is the number of people on the plane. For simplicity, I also assumed the plane is full (which is often the case), so all I had to source was the number of seats on different airplane models, which I retrieved from SeatGuru. I then filtered on the largest domestic airlines, and threw in Spirit for good measure (although you might not make it to your destination if you fly that airline, regardless of whether there's a doctor on your flight).

Take the largest airplane model/seat configuration in my dataset, the Boeing 777-300ER (77W) flown by United Airlines. There are 366 seats on the plane, leaving 364 passengers that could be doctors. The probability the first person is a doctor is 0.295%, so the probability they are NOT a doctor is 99.71%. The same goes for the second person. And the next. And so on, or 0.9971^364 = 34.12%. This is the probability that ALL other people on the flight are NOT doctors. So the probability at least one of them IS a doctor is 1 - .3412 = 65.88%.

You would need at least 237 seats on the plane to have greater than a 50/50 chance of having a doctor on board.

American, Delta, and United crowd the top of this list, but they also make up most of the bottom too, as their size of aircraft vary widely. Meanwhile JetBlue, Southwest, and Spirit all show up lower, but they have far less variance in the sizes of the planes they fly.

Airline	Airplane Model	# in Airplane	# Left	Prob		Key
United	Boeing 777-300ER (77W)	366	364	65.88%		American
United	Boeing 777-200 (772) V4	364	362	65.68%		Delta
American	Boeing 777-300ER (77W)	308	306	59.51%		JetBlue
Delta	Airbus A350-900 (359)	306	304	59.27%		Southwest
Delta	Airbus A330-300 (333)	293	291	57.67%		Spirit
Delta	Boeing 777-200ER/LR (77L)	291	289	57.42%		United
American	Airbus A330-300 (333)	291	289	57.42%
American	Boeing 787-9 (789)	285	283	56.66%
American	Boeing 777-200 (777) V2	273	271	55.10%
United	Boeing 777-200 (772) V3 Two Class Intl	267	265	54.29%
United	Boeing 777-200 (772) V2 Three Class Intl	261	259	53.47%
Delta	Boeing 767-300 (76P/76Q)	261	259	53.47%
American	Boeing 777-200 (777) V1	260	258	53.34%
United	Boeing 777-200 (772) V1 Three Class Intl	258	256	53.06%
United	Boeing 787-9 (789)	252	250	52.22%
American	Airbus A330-200 (332)	247	245	51.51%
Delta	Boeing 767-400ER (76D)	246	244	51.37%
United	Boeing 767-400ER (764) Intl	242	240	50.79%
Delta	Airbus A330-200 (332)	234	232	49.61%
Delta	Boeing 757-300 (75Y)	234	232	49.61%
Spirit	Airbus A321 (321) V2	228	226	48.71%
Delta	Boeing 767-300ER (76H/76Z)	226	224	48.41%
Delta	Boeing 767-300ER (76Z) V2	226	224	48.41%
American	Boeing 787-8 (788)	226	224	48.41%
United	Boeing 787-8 (788)	219	217	47.33%
Spirit	Airbus A321 (321) V1	218	216	47.17%
United	Boeing 767-300ER (76L) Two Class	214	212	46.54%
United	Boeing 757-300 (753) V1/V2	213	211	46.39%
Delta	Boeing 767-300ER (76L)	211	209	46.07%
American	Boeing 767-300 (763)	209	207	45.75%
Delta	Boeing 767-300ER (76T/76W)	208	206	45.59%
JetBlue	Airbus A321 (321) V2	200	198	44.29%
Delta	Boeing 757-200 (75D)	199	197	44.12%
Delta	Boeing 757-200 (75P)	193	191	43.12%
Delta	Airbus A321 (321)	192	190	42.95%
American	Boeing 757-200 (752) Domestic V2	188	186	42.28%
American	Airbus A321 (321) V3	187	185	42.11%
Spirit	Airbus A320 (320) V2	182	180	41.24%
American	Airbus A321 (321) V2	181	179	41.07%
Delta	Boeing 737-900ER (739)	180	178	40.90%
Delta	Boeing 757-200 (757)	180	178	40.90%
United	Boeing 737 MAX 9	179	177	40.72%
United	Boeing 737-900 (739) V3	179	177	40.72%
United	Boeing 737-900 (739) V4	179	177	40.72%
Spirit	Airbus A320 (320) V1	178	176	40.55%
United	Boeing 767-300ER (76L) Three Class	177	175	40.37%
American	Boeing 757-200 (752) International	176	174	40.19%
Southwest	Boeing 737 MAX 8 (7M8)	175	173	40.02%
Southwest	Boeing 737-800 (738)	175	173	40.02%
American	Boeing 737 MAX 8 (7M8)	172	170	39.48%
United	Boeing 757-200 (752) V1 Intl	169	167	38.94%
Delta	Boeing 757-200 (75G)	169	167	38.94%
Delta	Boeing 757-200 (75S)	168	166	38.76%
United	Boeing 737-900 (739) V1/V2	167	165	38.58%
United	Boeing 737-800 (738) V2	166	164	38.40%
United	Boeing 737-800 (738) V3	166	164	38.40%
United	Boeing 737-800 (738) V4	166	164	38.40%
Delta	Airbus A320 (320/32K) V2	160	158	37.30%
Delta	Boeing 737-800 (73H)	160	158	37.30%
American	Boeing 737-800 (738)	160	158	37.30%
JetBlue	Airbus A321 (321) Transcon	159	157	37.11%
Delta	McDonnell Douglas MD-90 (M90)	158	156	36.93%
United	Boeing 737-800 (738) V1	154	152	36.18%
United	Airbus A320 (320)	150	148	35.42%
Delta	Airbus A320 (320/32R) V1	150	148	35.42%
American	Airbus A320 (320)	150	148	35.42%
JetBlue	Airbus A320 (320)	150	148	35.42%
Delta	McDonnell Douglas MD-88 (M88)	149	147	35.23%
Spirit	Airbus A319 (319)	145	143	34.46%
Southwest	Boeing 737-700 (737)	143	141	34.07%
United	Boeing 757-200 (752) V2 PS	142	140	33.87%
American	McDonnell Douglas MD-80 (M80)	140	138	33.48%
Delta	Airbus A319 (319) V2	132	130	31.89%
United	Airbus A319 (319)	128	126	31.08%
American	Airbus A319 (319)	128	126	31.08%
United	Boeing 737-700 (737) V3	126	124	30.67%
United	Boeing 737-700 (737) Micronesia	124	122	30.26%
Delta	Boeing 737-700 (73W)	124	122	30.26%
United	Boeing 737-700 (737) Domestic	118	116	29.02%
Delta	Boeing 717-200 (717)	110	108	27.32%
American	Airbus A321 (32B) Transcon	102	100	25.58%
JetBlue	Embraer E-190 (E90)	100	98	25.14%
American	Embraer ERJ-190 (E90)	99	97	24.92%
American	Embraer ERJ-175 (E75)	80	78	20.58%
American	Bombardier CRJ-900 (CR9) V2	79	77	20.35%
United	Embraer EMB 175	76	74	19.64%
Delta	Embraer E-175 (E75)	76	74	19.64%
Delta	Bombardier CRJ-900 (CR9)	76	74	19.64%
American	Embraer ERJ-175 (E75) V1	76	74	19.64%
American	Bombardier CRJ-900 (CR9) V1	76	74	19.64%
American	Bombardier CRJ-900 (CR9) V3	76	74	19.64%
United	Bombardier Q400 V2	74	72	19.16%
United	Bombardier Q400 V1	71	69	18.44%
United	Embraer EMB 170	70	68	18.20%
United	Bombardier CRJ-700 V2	70	68	18.20%
Delta	Bombardier CRJ-700 (CR7) V2	70	68	18.20%
American	Bombardier CRJ-700 (CR7) V2	70	68	18.20%
Delta	Embraer E-170 (E70)	69	67	17.96%
Delta	Bombardier CRJ-700 (CR7) V3	69	67	17.96%
United	Bombardier CRJ-700 V1	66	64	17.23%
United	Bombardier CRJ-700 V3	66	64	17.23%
Delta	Bombardier CRJ-700 (CR7) V1	65	63	16.98%
American	Bombardier CRJ-700 (CR7) V1	63	61	16.49%
United	Bombardier CRJ-200 V1	50	48	13.22%
United	Bombardier CRJ-200 V2	50	48	13.22%
United	Embraer ERJ-145 V1	50	48	13.22%
United	Embraer ERJ-145 V2	50	48	13.22%
United	Bombardier Q300	50	48	13.22%
Delta	Bombardier CRJ-100/200	50	48	13.22%
American	Bombardier CRJ-200 (CR2)	50	48	13.22%
American	Embraer ERJ-145 (ER4)	50	48	13.22%
American	de Havilland Dash 8 (DH3)	46	44	12.19%
American	Embraer ERJ-140 (ERD)	44	42	11.67%
United	Embraer ERJ-135	37	35	9.82%
United	Bombardier Q200	37	35	9.82%
United	Saab 340B	34	32	9.02%
United	Embraer EMB-120 V1	30	28	7.94%
United	Embraer EMB-120 V2	30	28	7.94%