Respuesta :
Answer:
1/2
Step-by-step explanation:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT it's clear that 1/2 the outcomes result in at least 2 tails
:)
Binomial distribution has only two possible outcomes. The probability that there will be at least two tails when three coins are flipped is 0.5.
What is binomial distribution|?
The binomial distribution is a type of distribution that has only two possible outcomes. The probability of an event being successful when repeated n number of times is given by the formula,
[tex]P_{x} = ^nC_x\ p^{x} q^{n-x}[/tex]
where p and q are the probabilities of an event being a success or failure, n is the number of successes needed.
Given to us
Three coins are flipped,
We know that a coin follows a binomial distribution, therefore, we can write,
the probability of a tail coming up, p = 0.5
the probability of not a tail coming up, therefore heads, q = 0.5
We know the formula of the binomial distribution,
[tex]P_{x} = ^nC_x\ p^{x} q^{n-x}[/tex]
As we need to find the probability that at least two tails will come up, therefore, we can say that we want to find the probability of 0 or 1 tails coming up,
The probability that No tail will come up,
[tex]P_{(x=0)} = ^3C_0\ (0.5^{0})(0.5^{3-0})\\\\P_{(x=0)} = 0.125[/tex]
The probability of exactly one tail coming up,
[tex]P_{(x=1)} = ^3C_1\ (0.5^{1})(0.5^{3-1})\\\\P_{(x=1)} = 0.375[/tex]
The probability of 0 or 1 tails coming up
= probability that No tail will come up + probability of exactly one tail coming up
= 0.125 + 0.375
= 0.5
We know that sum of all the probability for an event is 1, therefore,
Probability that there will be at least two tails
= 1 - (probability of 0 or 1 tails coming up)
= 1 -0.5
= 0.5
Hence, the probability that there will be at least two tails when three coins are flipped is 0.5.
Learn more about Binomial distribution:
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