A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in Table 2 of Appendix and compare the table result with the computed result. (a) Find the probability of getting exactly three heads. (b) Find the probability of getting exactly two heads. (c) Find the probability of getting two or more heads. (d) Find the probability of getting exactly three tails.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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Binomial Probabilities: Coin Flip A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in Table 2 of Appendix and compare the table result with the computed result.

(a) Find the probability of getting exactly three heads.

(b) Find the probability of getting exactly two heads.

(c) Find the probability of getting two or more heads.

(d) Find the probability of getting exactly three tails.

 

TABLE 2 Binomial Probability Distribution C p'q" -
n,r
This table shows the probability of r successes in n independent trials, each with probability of success p.
n
r
.01
.05
.10
.15
.20
.25
.30
.35
.40
.45
.50
.55
.60
.65
.70
2
.980
.902
.810
.723
.640
.563
.490
.423
.360
.303
.250
.203
.160
.123
.090
1
.020
.095
.180
.255
.320
.375
.420
.455
.480
.495
.500
.495
.480
.455
.420
.000
.002
.010
.023
.040
.063
.090
.123
.160
.203
.250
.303
.360
.423
.490
3
.970
.857
.729
.614
.512
.422
.343
.275
.216
.166
.125
.091
.064
.043
.027
1
.029
.135
.243
.325
.384
.422
.441
.444
.432
.408
.375
.334
.288
.239
.189
.000
.007
.027
.057
.096
.141
.189
.239
.288
.334
.375
.408
.432
.444
.441
3
.000
.000
.001
.003
.008
.016
.027
.043
.064
.091
.125
.166
.216
.275
.343
4
.961
.815
.656
.522
.410
.316
.240
.179
.130
.092
.062
.041
.026
.015
.008
1
.039
.171
.292
.368
.410
.422
.412
.384
.346
.300
.250
.200
.154
.112
.076
.001
.014
.049
.098
.154
.211
.265
.311
.346
.368
.375
.368
.346
.311
.265
3
.000
.000
.004
.011
.026
.047
.076
.112
.154
.200
.250
.300
.346
.384
.412
4
.000
.000
.000
.001
.002
.004
.008
.015
.026
.041
.062
.092
.130
.179
.240
.951
.774
.590
.444
.328
.237
.168
.116
.078
.050
.031
.019
.010
.005
.002
1
.048
.204
.328
.392
.410
.396
.360
.312
.259
.206
.156
.113
.077
.049
.028
2
.001
.021
.073
.138
.205
.264
.309
.336
.346
.337
.312
.276
.230
.181
.132
3
.000
.001
.008
.024
.051
.088
.132
.181
.230
.276
.312
.337
.346
.336
.309
4
.000
.000
.000
.002
.006
.015
.028
.049
.077
.113
.156
.206
.259
.312
.360
.000
.000
.000
.000
.000
.001
.002
.005
.010
.019
.031
.050
.078
.116
.168
.941
.735
.531
.377
.262
.178
.118
.075
.047
.028
.016
.008
.004
.002
.001
1
.057
.232
.354
.399
.393
.356
.303
.244
.187
.136
.094
.061
.037
.020
.010
.001
.031
.098
.176
.246
.297
.324
.328
.311
.278
.234
.186
.138
.095
.060
.000
.002
.015
.042
.082
.132
.185
.236
.276
.303
.312
.303
.276
.236
.185
4
.000
.000
.001
.006
.015
.033
.060
.095
.138
.186
.234
.278
.311
.328
.324
.000
.000
.000
.000
.002
.004
.010
.020
.037
.061
.094
.136
.187
.244
.303
.000
.000
.000
.000
.000
.000
.001
.002
.004
.008
.016
.028
.047
.075
.118
Σ
7
.932
.698
.478
.321
.210
.133
.082
.049
.028
.015
.008
.004
.002
.001
.000
9:50 PM Sun Jun 20
ull ?1 5% O
A3 of 695
Transcribed Image Text:TABLE 2 Binomial Probability Distribution C p'q" - n,r This table shows the probability of r successes in n independent trials, each with probability of success p. n r .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 2 .980 .902 .810 .723 .640 .563 .490 .423 .360 .303 .250 .203 .160 .123 .090 1 .020 .095 .180 .255 .320 .375 .420 .455 .480 .495 .500 .495 .480 .455 .420 .000 .002 .010 .023 .040 .063 .090 .123 .160 .203 .250 .303 .360 .423 .490 3 .970 .857 .729 .614 .512 .422 .343 .275 .216 .166 .125 .091 .064 .043 .027 1 .029 .135 .243 .325 .384 .422 .441 .444 .432 .408 .375 .334 .288 .239 .189 .000 .007 .027 .057 .096 .141 .189 .239 .288 .334 .375 .408 .432 .444 .441 3 .000 .000 .001 .003 .008 .016 .027 .043 .064 .091 .125 .166 .216 .275 .343 4 .961 .815 .656 .522 .410 .316 .240 .179 .130 .092 .062 .041 .026 .015 .008 1 .039 .171 .292 .368 .410 .422 .412 .384 .346 .300 .250 .200 .154 .112 .076 .001 .014 .049 .098 .154 .211 .265 .311 .346 .368 .375 .368 .346 .311 .265 3 .000 .000 .004 .011 .026 .047 .076 .112 .154 .200 .250 .300 .346 .384 .412 4 .000 .000 .000 .001 .002 .004 .008 .015 .026 .041 .062 .092 .130 .179 .240 .951 .774 .590 .444 .328 .237 .168 .116 .078 .050 .031 .019 .010 .005 .002 1 .048 .204 .328 .392 .410 .396 .360 .312 .259 .206 .156 .113 .077 .049 .028 2 .001 .021 .073 .138 .205 .264 .309 .336 .346 .337 .312 .276 .230 .181 .132 3 .000 .001 .008 .024 .051 .088 .132 .181 .230 .276 .312 .337 .346 .336 .309 4 .000 .000 .000 .002 .006 .015 .028 .049 .077 .113 .156 .206 .259 .312 .360 .000 .000 .000 .000 .000 .001 .002 .005 .010 .019 .031 .050 .078 .116 .168 .941 .735 .531 .377 .262 .178 .118 .075 .047 .028 .016 .008 .004 .002 .001 1 .057 .232 .354 .399 .393 .356 .303 .244 .187 .136 .094 .061 .037 .020 .010 .001 .031 .098 .176 .246 .297 .324 .328 .311 .278 .234 .186 .138 .095 .060 .000 .002 .015 .042 .082 .132 .185 .236 .276 .303 .312 .303 .276 .236 .185 4 .000 .000 .001 .006 .015 .033 .060 .095 .138 .186 .234 .278 .311 .328 .324 .000 .000 .000 .000 .002 .004 .010 .020 .037 .061 .094 .136 .187 .244 .303 .000 .000 .000 .000 .000 .000 .001 .002 .004 .008 .016 .028 .047 .075 .118 Σ 7 .932 .698 .478 .321 .210 .133 .082 .049 .028 .015 .008 .004 .002 .001 .000 9:50 PM Sun Jun 20 ull ?1 5% O A3 of 695
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