Fifty-two percent of the women in the UK play video games regularly. You randomly select seven women in the UK. Find the probability that the number of women in the UK who are gamers is

(a) exactly four,

(b) at least five,

(c) less than four.

Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Table 2 in Appendix B

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Table 2-Binomial Distribution This table shows the probability of x successes in n independent trials, each with probability of success p. .154 026 200 041 P n x .01 .05 .10 .15 .20 -25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 20 980 902 810 723 .640 563 490 423 360 .303 .250 .203 160 123 .090 .063 040 023 010 .002 1 .020 .095 180 255 .320 375 420 .455 .480 495 500 495 480 455 420 .375 .320 .255 180 .095 2.000 .002 .010 .023 .040.063 .090 .123 .160 .203 .250 .303 360 .423 490 .563 640 723 810 .902 3 0.970 857 729 614 512 422 343 275 216.166 125 091 064 .043 .027 .016 .008 .003 .001 .000 1 .029 135 .243 325 .384 422 441 444 432 408 .375 .334 .288 .239 .189 .141 .096 057 027 .007 2.000 .007 .027 .057 .096 141 189 239 288 334 .375 .408 432 444 441 422 384 325 243 .135 3.000 .000 .001 .003 .008 .016 .027 .043 .064 091 .125 166 216 275 343 .422 512 614 .729 .857 4 0961 815 .656 522 .410 .316 240 179 130 092 .062 .041 .026 .015 .008 .004 .002 .001 .000 .000 1 .039 171 .292 .368 .410 .422 412 384 346 300 250 200 154 112 076 047 026 .011 .004 .000 2001 014 .049 098 154 211 265 311 346 368 375 368 346 311 .265 211 154 .098 .049 .014 3 .000 .000 .004 .011 .026 .047 076 .112 .250 .300 .346 384 412 422 .410 .368 .292 .171 4 .000 .000 .000 .001.002 .004 .008 .015 062 .092 .130 .179 240 316 .410 522 .656 .815 5 0.951 774 590 .444 328 237 .168 .116 078 050 031 019 .010 .005 .002 .001 .000 .000 .000 .000 1 .048 204 328 392 410 396 360 .312 .259 206 156 113 .077 .049 028 015 .006 .002 .000 .000 2 .001 .021 .073 138 205 264 309 336 346 337 .312 .276 230 181 132 088 051 024 .008 .001 3 000 001 .008 .024 .051 .088 132 .181 230 276 .312 .337 .346 336 309 264 205 138 .073 .021 4 .000 .000 .000 .002 .006 .015 028 049 077 .113 .156 .206 259 .312 .360 396 .410 392 328 204 5 .000 .000 .000 .000 .000 .001 002 .005 010 019 031 050 078 116 168 237 328 .444 590 774 60941 735 .531 377 .262 .178 118 .075 .047 .028 .016 .008 .004 .002 .001 .000 .000 .000 .000 .000 1 .057 232 354 399 .393 356 303 244 187 136 .094 .061 037 020 010 .004 .002 .000 .000 .000 2001 031 .098 176 246 297 324 .328 .311 .278 .234 .186 138 .095 .060 .033 .015 .006 .001 .000 3 .000 .002 .015 042 .082 132 185 236 276 .303 .312 .303 .276 236 185 132 082 042 .015 .002 4 .000 .000 .001 006 .015 .033 060 095 138 186 .234 .278 .311 .328 324 297 246 176 098 .031 5 .000 .000 .000 .000 .002 .004 .010 020 .037 061 .094 136 .187 244 303 356 393 399 354 .232 6 .000 .000 .000 .000 .000 .000 .001 002 004 008 .016 .028 .047 .075 118.178 262 377 .531 735 049 .028 015 008 004 .002 .001 .000 .000 .000 .000 .000 .000 185 131 .087 .055 .032 .017 008 .004 .001 .000 .000 .000 .000 299 261 214 164 .117 .077 .047 .025 .012 .004 .001 .000 .000 268 290 292 .273 239 194 144 097 058 .029 .011 .003 .000 239 273 292 290 268 227 173 115 062 117 .164 214 261 299 318 311 275 210 124 .041 6 .000 .000 .000 .000 .000 .001 .004 .008 .017 032 055 087 .131 .185 .247 .311 .367 396 .372 .257 7.000 .000 .000 .000 .000 .000 .000 .001 .002 .004 .008 .015 .028 049 082 133 .210 .321 .478 698 4 7 0.932 698 478 321 210 133 082 1 .066 .257 .372 .396 367 .311 .247 2002 .041 .124 210 275 .311 .318 3 000 004 .023 062 .115 173 227 000 .000 003 .011 .029 .058 .097 5000 .000 .000 .001 .004 .012 .025 .047 .077 144 194 023 .004 8 0 .923 .663 430 272 168 100 .058 .032 .017 .008 .004 .002 .001 .000 .000 .000 .000 .000 .000 .000 1075 279 383 385 336 267 .198 137 .090 .055 .031 .016 .008 .003 .001 .000 .000 .000 .000 .000 2003 051 149 238 294 .311 296 .259 209 157 109 070 041 022 .010.004 .001 .000 .000 .000 3 000 005.033 .084 .147 .208 254 .279 4 .000 .000 .005 018 .046 087 136 188 279 .257 219 172 .124 .081 .047 .023 .009 .003 .000 .000 232 .263 .273 .263 .232 .188 136 087 046 018 .005 .000 5 .000 .000 .000 003 .009 .023 .047 .081 124 172 219 257 279 279 254 208 147 084 033 .005 6 .000 .000 .000 .000 .001 004 010 022 .041 070 109 157 209 259 296 .311 294 238 .149 .051 7.000 .000 .000 .000 .000 .000 .001 .003 .008 .016 .031 .055 .090 137 198 267 336 385 383 .279 8.000 .000 .000 .000 .000 .000 .000 .000 .001 002 004 .008 017 .032 .058 100 168 272 430 663 9 0914 630 387 232 .134 075 040 021 010 005 002 .001 .000 .000 .000 .000 .000 .000 .000 .000 1.083 299 .387 368 302 225 .156 .100 .060 034 .018 .008 .004 .001 .000 .000 .000 .000 .000 .000 2003 .063.172 260 302 300 267 216 .161 111 .070 .041 .021 .010 004 .001 .000 .000 .000 .000 3 .000 .008 .045 .107.176 234 267 272 251 212 164 116 .074 .042 .021 .009 .003 .001 .000 .000 4.000.001.007 .028 .066 117 172 219 .251 260 246 213 167 118 .074 .039 .017 .005 .001 .000 5 .000 .000 .001 .005 .017 .039 .074 118 .167 213 246 260 251 219 172 117 .066 .028 .007 .001 116 .164 212 251 272 267 234 .176 .107 .045 .008 .000 .000 .000 .000 .000 .001 .004 .010 .021 041 .070 .111 .161 216 267 300 .302 260 172.063 8 .000 .000 .000 .000 .000 .000 .000 .001 .004 .008 .018 .034 .060 100 156 225 302 368 .387 .299 9 .000 .000 .000 .000 .000 .000 .000 .000 .000 001 002 005.010 .021 .040 075 134 232 387 630. 6 .000 .000 .000 .001 .003 .009 .021 042 .074 7