Question

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 the binomial probability distribution table. (Enter your answers to three decimal places.)

(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.

Answer 1

Binocneal distrebution foronela ex n-ne n! (non)! MT P (n) = - p q r-ne conene, n= the number of trials x = the neember of successes desined P = probability Do getting success in one I treal q=1-p = the probability of getting a faéline in one freol. probability of getting enactly three heads there, n=3 p = Ž 1 x=3 q= 1 / 2 so, p(n=3) = - 6) = * = 0.125 b) probality of getting enactly two heads W -3 31 3-21 - Hene, n=3 p = 1² m=29= 50, PCr=2) = 3! Go!)8-2 (3-2)! 2! (2) = 3 *[ 54)' = 3x Ś - 0.375 probability of getting two on cnone heels c) o probability camera) + pēr-s)< 5 + Ź 0.500

LLLL d) fail TO probabé lety or getting exactly three Here, n=3 p = 1/2 1 x=3 a= 2 / 2 30, P(x+3) = 3! (*5) = (3-4 = 0.125 3 3-3
You can look up the probability from this binomial probability distrubution table,

first search value of n

then go to value of x on column and value of p on row.

Numbers in the table represent p(X=x) for a binomial distribution with n trials and probability of success p. Binomial probabilities: X 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 Q)241-p-* 1 0 0.900 1 0 .100 2 0 0 .810 1 0 .180 0.010 0.729 0.243 0.027 0.001 0.656 0.292 0.049 0.004 0.000 50 0.590 1 0 .328 2 0 .073 3 0 .008 | 0.000 0.000 0.531 0.354 0.098 0.015 0.001 0.000 1 0.000 0.478 0.372 0.124 1 0.023 4 0 .003 5 0 .000 6 0.000 7 0 .000 0.800 0.200 0.640 0.320 0.040 0.512 0.384 0.096 0.008 0.410 0.410 0.154 0.026 0.002 0.328 0.410 0.205 0.051 0.006 0.000 0.262 0.393 0.246 0.082 0.015 0.002 0.000 0.210 0.367 0.275 0.115 0.029 0.004 0.000 0.000 0.750 0.250 0.563 0.375 0.063 0.422 0.422 0.141 0.016 0.316 0.422 0.211 0.047 0.004 0.237 0.396 0.264 0.088 0.015 0.001 0.178 0.356 0.297 0.132 0.033 0.004 0.000 0.133 0.311 0.311 0.173 0.058 0.012 0.001 0.000 0.700 0.600 0.300 0.400 0.490 0.360 0.420 0.480 0.090 0.160 0.343 0.216 0.441 0.432 0.189 0.288 0.027 0.064 0.240 0.130 0.412 0.346 0.265 0.346 0.076 0.154 0.008 0.026 0.168 0.078 0.360 0.259 0.309 0.346 0.132 0.230 0.028 0.077 0.002 0.010 0.118 0.047 0.303 0.187 0.324 0.311 0.185 0.276 0.060 0.138 0.010 0.037 0.001 0.004 0.082 0.028 0.247 0.131 0.318 0.261 0.227 0.290 0.097 0.194 0.025 0.077 0.004 0.017 0.000 0.002 0.500 0.400 0.500 0.600 0.250 0.160 0.500 0.480 0.250 0.360 0.125 0.064 0.375 0.288 0.375 0.432 0.125 0.216 0.063 0.026 0.250 0.154 0.375 0.346 0.250 0.346 0.063 0.130 0.031 0.010 0.156 0.077 0.313 0.230 0.313 0.346 0.156 0.259 0.031 0.078 0.016 0.004 0.094 0.037 0.234 0.138 0.313 0.276 0.234 0.311 0.094 0.187 0.016 0.047 0.008 0.002 0.055 0.017 0.164 0.077 0.273 0.194 0.273 0.290 0.164 0.261 0.055 0.131 0.008 0.028 0.300 0.700 0.090 0.420 0.490 0.027 0.189 0.441 0.343 0.008 0.076 0.265 0.412 0.240 0.002 0.028 0.132 0.309 0.360 0.168 0.001 0.010 0.060 0.185 0.324 0.303 0.118 0.000 0.004 0.025 0.097 0.227 0.318 0.247 0.082 0.250 0.750 0.063 0.375 0.563 0.016 0.141 0.422 0.422 0.004 0.047 0.211 0.422 0.316 0.001 0.015 0.088 0.264 0.396 0.237 0.000 0.004 0.033 0.132 0.297 0.356 0.178 0.000 0.001 0.012 0.058 0.173 0.311 0.311 0.133 0.200 0.800 0.040 0.320 0.640 0.008 0.096 0.384 0.512 0.002 0.026 0.154 0.410 0.410 0.000 0.006 0.051 0.205 0.410 0.328 0.000 0.002 0.015 0.082 0.246 0.393 0.262 0.000 0.000 0.004 0.029 0.115 0.275 0.367 0.210 0.100 0.900 0.010 0.180 0.810 0.001 0.027 0.243 0.729 0.000 0.004 0.049 0.292 0.656 0.000 0.000 0.008 0.073 0.328 0.590 0.000 0.000 0.001 0.015 0.098 0.354 0.531 0.000 0.000 0.000 0.003 0.023 0.124 0.372 0.478 osen UN (continued