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Twenty-six biased coins are flipped once. The coins are weighted so that the probability of a head with any coin is 0.3. What is the probability of getting at least 15 heads

Respuesta :

Answer:

The probability of getting at least 15 heads in 26 tosses is 0.0030.

Step-by-step explanation:

Let X = number of heads.

The probability of getting a head is, P (X) = p = 0.30.

The number of coins flipped is, n = 26.

The random variable X follows a Binomial distribution with parameter n = 26 and p = 0.3.

The probability mass function of a Binomial distribution is:

[tex]P(X =x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, 3...[/tex]

Compute the probability of getting at least 15 heads as follows:

P (X ≥ 15) = 1 - P (X < 15)

               [tex]=1-\sum_{x=0}^{x=14} P (X=x)\\=1-\sum_{x=0}^{x=14} [{26\choose x}(0.30)^{x}(1-0.30)^{26-x}]\\=1-0.9970\\=0.0030[/tex]

Thus, the probability of getting at least 15 heads in 26 tosses is 0.0030.

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