Question

Kat and Jasmine have gathered data on a tennis game and has determined that typically 21% of the players get the serve within service line in the first shot. If you watch 6 games, how likely it is that two consecutive games will get the serve in the first time. Simulate this 10 times using the random digit below, use your findings to estimate this probability. Make sure to explain the simulation process.

Line 130 69051 64817 87174 09517 84534 06489 87201 97245

Line 131 05007 16632 81194 14873 04197 85576 45195 96965

Line 132 68732 55259 84292 08796 43165 93739 31685 97150

State —>

Plan ——>

Do ——>

Conclude ——>

Answer 1

Solution

Just for convenience of presentation, let X represent the event that the players get the serve within service line in the first shot and Y represent the event that the players did not get the serve within service line in the first shot.

Assignment of Random Numbers

01 to 21 for X and 22 to 99, 00 for Y.

Actual Simulation

Following codes are used in the table below:

RN: Random Number; G: Game

Run #	Chosen RN						X or Y						# of Consecutive X’s
	G1	G2	G3	G4	G5	G6	G1	G2	G3	G4	G5	G6
1	69	05	16	48	17	87	Y	X	X	Y	X	Y	1
2	17	40	95	17	84	53	X	Y	Y	X	Y	Y	0
3	40	64	89	87	20	19	Y	Y	Y	Y	X	X	1
4	72	45	05	00	71	66	Y	Y	X	X	Y	Y	1
5	32	81	19	41	48	73	Y	Y	X	Y	Y	Y	0
6	04	19	78	55	76	45	X	X	Y	Y	Y	Y	1
7	19	59	69	65	68	73	X	Y	Y	Y	Y	Y	0
8	25	52	49	84	29	20	Y	Y	Y	Y	Y	X	0
9	87	96	43	16	59	37	Y	Y	Y	X	Y	Y	0
10	39	31	68	59	71	50	Y	Y	Y	Y	Y	Y	0

Thus, out 60 simulated games, 4 resulted in X. Hence, the simulated probability of two consecutive games getting the serve in the first time = 4/60 = 0.0667 ANSWER

DONE