Question

Three coins are flipped. What is the probability that there will be at least two tails?

Answer 1

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

:)

Answer 2

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,

$P_{x} = ^nC_x\ p^{x} q^{n-x}$

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,

$P_{x} = ^nC_x\ p^{x} q^{n-x}$

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,

$P_{(x=0)} = ^3C_0\ (0.5^{0})(0.5^{3-0})\\\\P_{(x=0)} = 0.125$

The probability of exactly one tail coming up,

$P_{(x=1)} = ^3C_1\ (0.5^{1})(0.5^{3-1})\\\\P_{(x=1)} = 0.375$

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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