Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes. n=4 and p=0.25 a. Determine P(X=2) using the binomial probability formula.b. Determine P(X=2) using a table of binomial probabilities. Compare this answer to part (a). a. Using the binomial formula, P(X=2) is ____________.(Round to three decimal places as needed.) b. Using the binomial probability table, P(X=2) is _______.(Round to three decimal places as needed.) Compare this result to the probability found in part (a). Choose the correct answer below. A.The two probabilities are exactly equal at 3 decimal places.B.The two probabilities are approximately equal at 3 decimal places.C.The probability from part (a) is much larger than the probability from part (b).D.The probability from part (b) is much larger than the probability from part (a). 0.20.250.30.40.50.60.70.750.80.90.900 0.800 0.750 0.700 0.600 0.500 0400 0.300 0.250 0.200 0.1000,100 0.200 0.250 0.300 0.400 0.500 0,600 0.700 0.750 0.800 0.9002 00.8 10 0.640 0.563 0.490 0.360 0.250 0.160 0.090 0.063 0.040 0.0100.180 0.320 0.375 0.420 0.480 0500 0.480 0.420 0.375 0.320 0.1800.010 0.040 0.063 0.090 0.160 0.250 0.360 0.490 0563 0.640 0.81023 00.729 0.512 0.422 0.343 0.216 0.125 0.064 0.027 0.016 0.008 0.0010.243 0.384 0.422 0.441 0.432 0.375 0.288 0.189 0.141 0.096 0.0270.027 0.096 0.141 0.189 0.288 0.375 0,432 0441 0422 0.384 0.24330.001 0.008 0.016 0.027 0.064 0.125 0.216 0343 0422 0.512 0.7294 00.656 0.4 10 0.316 0.240 0.130 0.063 0.026 0.008 0.004 0.002 0.0000.292 0.410 0.422 0.412 0.346 0.250 0.154 0.076 0,047 0.026 0.0040.049 0.154 0.211 0.265 0.346 0.375 0.346 0265 0.211 0.154 0.04930.004 0.026 0.047 0.076 0.154 0.250 0.346 0.412 0422 0.410 0.29240.000 0.002 0.004 0.008 0D26 0.063 0.130 0240 0316 0.410 0.6565 00.590 0.328 0.237 0.168 0.078 0031 0.010 0.002 0.001 0.000 0.0000.328 0.410 0.396 0.360 0.259 0.156 0.07T7 0.028 0015 0.006 0.0000.073 0.205 0.264 0.309 0346 0.312 0.230 0.132 0.088 0.051 0.00830.008 0.031 0.088 0.132 0.230 0.312 0.346 0309 0.264 0.205 0.0730.000 0.006 0.015 0.028 0.077 0.156 0.259 0.360 0.396 0410 0.328450.000 0.000 0.001 0.002 0.010 0.031 0.078 0.168 0.237 0.328 0.5906 00.531 0.262 0.178 0.118 0.047 0.016 0.004 0.001 0.000 0.000 0.0000.354 0.393 0.356 0.303 0.187 0.094 0.037 0.010 0.004 0.002 0.0000.098 0.246 0.297 0.324 03|| 0.234 0.138 0060 0033 0015 0.0010,015 0.082 0.132 0.185 0.276 0313 0.276 0.183 0.132 0.082 00150.001 0.015 0.033 0.060 0.138 0.234 0.311 0.324 0.297 0.246 0.0980.000 0.002 0.004 0.010 0.037 0.094 0.187 0.303 0.356 0.393 0.3540.000 0.000 0.000 0.001 0.004 0.016 0.047 0.118 0.178 0.262 0.5312347 00.478 0.210 0.133 0.082 0.028 0.008 0.002 0.000 0.000 0.000 0.0000.372 0.367 0.311 0.247 0.131 0.055 0.017 0.004 0.001 0.000 0.0000.124 0.275 0.311 0.318 0.261 0.164 0.07n 0025 0012 0001 000030.023 0.115 0.173 0.227 0.290 0.273 0.194 0.097 0058 0.029 00030,003 0.029 0.058 0.097 0.194 0.273 0.290 0227 0.173 0.115 0.0230.000 0.004 0.012 0.025 0.077 0.164 0.261 0318 0.311 0.275 0.1240.000 0.000 0.001 0.004 0.D17 0.055 0.131 0247 0.311 0.367 0.3720.000 0.000 0.000 0.000 0002 0.008 0.028 0.082 0.133 0.210 0.4784

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Description: Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes. n=4 and p=0.25 a. Determine P(X=2) using the binomial probability formula.b. Determine P(X=2) using a table of bin

Given: n = 4 p = 0.25 X denote the total number of successes

Answered: Shown below are the number of trials…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes.

n=4 and p=0.25

a. Determine P(X=2) using the binomial probability formula.

b. Determine P(X=2) using a table of binomial probabilities. Compare this answer to part (a).

a. Using the binomial formula, P(X=2) is ____________.

(Round to three decimal places as needed.)

b. Using the binomial probability table, P(X=2) is _______.

(Round to three decimal places as needed.)

Compare this result to the probability found in part (a). Choose the correct answer below.

A.The two probabilities are exactly equal at 3 decimal places.

B.The two probabilities are approximately equal at 3 decimal places.

C.The probability from part (a) is much larger than the probability from part (b).

D.The probability from part (b) is much larger than the probability from part (a).

0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.75
0.8
0.9
0.900 0.800 0.750 0.700 0.600 0.500 0400 0.300 0.250 0.200 0.100
0,100 0.200 0.250 0.300 0.400 0.500 0,600 0.700 0.750 0.800 0.900
2 0
0.8 10 0.640 0.563 0.490 0.360 0.250 0.160 0.090 0.063 0.040 0.010
0.180 0.320 0.375 0.420 0.480 0500 0.480 0.420 0.375 0.320 0.180
0.010 0.040 0.063 0.090 0.160 0.250 0.360 0.490 0563 0.640 0.810
2
3 0
0.729 0.512 0.422 0.343 0.216 0.125 0.064 0.027 0.016 0.008 0.001
0.243 0.384 0.422 0.441 0.432 0.375 0.288 0.189 0.141 0.096 0.027
0.027 0.096 0.141 0.189 0.288 0.375 0,432 0441 0422 0.384 0.243
3
0.001 0.008 0.016 0.027 0.064 0.125 0.216 0343 0422 0.512 0.729
4 0
0.656 0.4 10 0.316 0.240 0.130 0.063 0.026 0.008 0.004 0.002 0.000
0.292 0.410 0.422 0.412 0.346 0.250 0.154 0.076 0,047 0.026 0.004
0.049 0.154 0.211 0.265 0.346 0.375 0.346 0265 0.211 0.154 0.049
3
0.004 0.026 0.047 0.076 0.154 0.250 0.346 0.412 0422 0.410 0.292
4
0.000 0.002 0.004 0.008 0D26 0.063 0.130 0240 0316 0.410 0.656
5 0
0.590 0.328 0.237 0.168 0.078 0031 0.010 0.002 0.001 0.000 0.000
0.328 0.410 0.396 0.360 0.259 0.156 0.07T7 0.028 0015 0.006 0.000
0.073 0.205 0.264 0.309 0346 0.312 0.230 0.132 0.088 0.051 0.008
3
0.008 0.031 0.088 0.132 0.230 0.312 0.346 0309 0.264 0.205 0.073
0.000 0.006 0.015 0.028 0.077 0.156 0.259 0.360 0.396 0410 0.328
4
5
0.000 0.000 0.001 0.002 0.010 0.031 0.078 0.168 0.237 0.328 0.590
6 0
0.531 0.262 0.178 0.118 0.047 0.016 0.004 0.001 0.000 0.000 0.000
0.354 0.393 0.356 0.303 0.187 0.094 0.037 0.010 0.004 0.002 0.000
0.098 0.246 0.297 0.324 03|| 0.234 0.138 0060 0033 0015 0.001
0,015 0.082 0.132 0.185 0.276 0313 0.276 0.183 0.132 0.082 0015
0.001 0.015 0.033 0.060 0.138 0.234 0.311 0.324 0.297 0.246 0.098
0.000 0.002 0.004 0.010 0.037 0.094 0.187 0.303 0.356 0.393 0.354
0.000 0.000 0.000 0.001 0.004 0.016 0.047 0.118 0.178 0.262 0.531
2
3
4
7 0
0.478 0.210 0.133 0.082 0.028 0.008 0.002 0.000 0.000 0.000 0.000
0.372 0.367 0.311 0.247 0.131 0.055 0.017 0.004 0.001 0.000 0.000
0.124 0.275 0.311 0.318 0.261 0.164 0.07n 0025 0012 0001 0000
3
0.023 0.115 0.173 0.227 0.290 0.273 0.194 0.097 0058 0.029 0003
0,003 0.029 0.058 0.097 0.194 0.273 0.290 0227 0.173 0.115 0.023
0.000 0.004 0.012 0.025 0.077 0.164 0.261 0318 0.311 0.275 0.124
0.000 0.000 0.001 0.004 0.D17 0.055 0.131 0247 0.311 0.367 0.372
0.000 0.000 0.000 0.000 0002 0.008 0.028 0.082 0.133 0.210 0.478
4

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