To compare two varieties of barley b1 and b2 an experiment i

To compare two varieties of barley (b1 and b2), an experiment is conducted on five equally sized plots. For each plot, we flip a coin to determine which variety to use. We use variety b1 if the coin comes up heads, and variety b2 if the coin comes up tails. Suppose that the probability that the coin lands on heads is 0.6. Compute the probability that b1 is used only in the first plot: b1 is used in all five plots: the same variety of barley is used in all five plots.

Solution

Let H = heads
T = tails.

a)

Thus means a sequence of

P(HTTTT) = 0.6*(1-0.6)*(1-0.6)*(1-0.6)*(1-0.6) = 0.01536 [ANSWER]

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b)

This means a sequence of

P(HHHHH) = 0.6*0.6*0.6*0.6*0.6 = 0.07776 [ANSWER]

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C)

P(all same) = P(HHHHH) + P(TTTTT) = 0.6*0.6*0.6*0.6*0.6 + (1-0.6)*(1-0.6)*(1-0.6)*(1-0.6)*(1-0.6) = 0.088 [ANSWER]