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We’ll now discuss something called Bayes’ Theorem. Bayes' Theorem, by definition, provides a way to revise and update probabilities as you gain more information. It allows you to determine the probability of event B occurring given that event A has occurred and is denoted P(B | A):P(B | A) = P(A | B) * P(B) / P(A)When flipping a coin twice, what is the probability of getting two heads in a row given that you know at least one flip results in a head? The Bayes’ equation for this problem is already provided below. Select the best answer.P(2H | 1H) = P(1H | 2H) * P(2H) / P(1H)

Question

We’ll now discuss something called Bayes’ Theorem. Bayes' Theorem, by definition, provides a way to revise and update probabilities as you gain more information. It allows you to determine the probability of event B occurring given that event A has occurred and is denoted P(B | A):P(B | A) = P(A | B) * P(B) / P(A)When flipping a coin twice, what is the probability of getting two heads in a row given that you know at least one flip results in a head? The Bayes’ equation for this problem is already provided below. Select the best answer.P(2H | 1H) = P(1H | 2H) * P(2H) / P(1H)

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Solution

To solve this problem, we first need to determine the values for P(1H | 2H), P(2H), and P(1H).

  1. P(1H | 2H) is the probability of getting at least one head given that you got two heads. This is obviously 1, because if you got two heads, you definitely got at least one head.

  2. P(2H) is the probability of getting two heads in two flips. There are 4 possible outcomes when flipping a coin twice (HH, HT, TH, TT), so the probability of getting two heads is 1/4.

  3. P(1H) is the probability of getting at least one head in two flips. There are 3 outcomes that include at least one head (HH, HT, TH), so the probability is 3/4.

Now we can substitute these values into the Bayes' Theorem equation:

P(2H | 1H) = P(1H | 2H) * P(2H) / P(1H) = 1 * (1/4) / (3/4) = 1/3.

So, the probability of getting two heads in a row given that you know at least one flip results in a head is 1/3.

This problem has been solved

Similar Questions

Probability is a measure of how likely an event is to occur. The probability of a certain event occurring is defined as the number of ways the certain event can occur or the number of favourable outcomes, divided by the total number of possible outcomes.If we flip a coin once, the probability of it landing on heads is 1/2. 1 being the favourable outcome (H) and 2 being all possible outcomes (H, T). We can write this out like so:P(1H) = ½When you flip a coin twice, the possible outcomes are: HH, HT, TH, and TT. If you flip a coin twice, what’s the probability of obtaining at least one head? Select the best answer.

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Two coins are tossed, the probability of getting at least one head is

Two coins are tossed, the probability of getting at least one head isans.

What is the probability of getting 2 heads if you flip a coin 3 times.

1/3

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