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11. [8] The probability that the coin lands tails is 40%. Because the probability is not...


11. [8] The probability that the coin lands tails is 40%. Because the probability is not 50% this is often called a trick coi
11. [8] The probability that the coin lands tails is 40%. Because the probability is not 50% this is often called a trick coin. Let the random variable y count the number of tails out of a sample of three tosses. Find the probabilities of each value of the random variable Y. Show the work used to get answers. 0 1 2 3 Y PY)
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Ans 1)

Probability of success (drawing a tail) = 40/100 = 0.4

Total number of trials n = 3

Formula to calculate Binomial probability:

P(Y=y) = \binom{n}{y}p^y(1-p)^{n-y}

Probability when there is 0 tail:

P(Y=0) = \binom{3}{0}(0.4)^0(1-0.4)^{3-0}

= 1\times1\times(0.6)^{3}

= 0.216

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Probability when there is 1 tail:

P(Y=1) = \binom{3}{1}(0.4)^1(1-0.4)^{3-1}

= 3\times0.4\times(0.6)^{2}

=0.432

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Probability when there is 2 tail:

P(Y=2) = \binom{3}{2}(0.4)^2(1-0.4)^{3-2}

= 3\times0.4^2\times(0.6)^{1}

=0.288

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Probability when there is 3 tail:

P(Y=3) = \binom{3}{3}(0.4)^3(1-0.4)^{3-3}

= 1\times0.4^3\times(0.6)^{0}

=0.064

Y 0 1 2 3
P(Y) 0.2160 0.4320 0.2880 0.0640
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