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If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 1 heads?

Sagot :

Thaprettyebony
0.98 is the probability of getting 1 Head in 6 tosses.
Tundexi

Probability of getting exactly 1 heads is 0.094.

As a binomial model, there are only two outcomes, the heads & tails

For a coin, the probability of getting heads or tails = 1 /2 = 0.5

Let 'X' be the no of heads obtained

Let :p" be the probability of getting heads

X~Bin (n=6, p = 0.5)

P (X=x) = [tex]nCx * p^{x}* (1-p)^{n-x}[/tex]

P (X=x) = [tex]6Cx* 0.5^{x} * (1-0.5)^{6-x}[/tex]

P (X=x) = [tex]6Cx* 0.5^{x} * (0.5)^{6-x}[/tex]

Note that we need to find probability of getting exactly 1 heads. So we will input the figures

P (X=1) =  [tex]6C1 * 0.5^{1} * 0.5^{6-1}[/tex]

P (X=1) = [tex]6C1 * 0.5^{1} * 0.5^{5}[/tex]

P (X=1) = [tex]6 * 0.5 * 0.03125[/tex]

P (X=1) = 0.09375

P (X=1) = 0.094

Therefore, the probability of getting exactly 1 heads is 0.094.

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