two six sided dice are rolled and the sum of the tow dice equals 7. what is the probability that one die is a 3

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20-12-2022
Mathematics

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two six sided dice are rolled and the sum of the tow dice equals 7. what is the probability that one die is a 3

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-22T13:25:26-05:00

The probability that one die is a 3 is 0.167.

The concept of the conditional probability formula is one of the quintessential concepts in probability theory. The conditional probability formula gives the measure of the probability of an event, say B given that another event, say A has occurred.

The Bayes' theorem is used to determine the conditional probability of event A, given that event B has occurred, by knowing the conditional probability of event B, given that event A has occurred, also the individual probabilities of events A and B.

Note: In case P(B)=0, the conditional probability of P(A | B) is undefined. (the event B did not occur).

Number of ways to roll out two dice = 6 x 6 = 36

Let A be the event in which the sum of the two dice is 7.

∴ P(A) = 6/36

Let B be the event in which one die is 3.

∴ P(B) = 10/36

Let P(B∩A) be the event in which the sum of the dice is 7 and one die is 3.

P(B∩A) = 1/36

Applying the formula of conditional probability,

P (B|A) = P (A ∩ B)⁄P (A)

= 1/36 * 6/36 = 1/6 = 0.167

Thus, the probability that one die is a 3 is 0.167.

To learn more about probability, visit brainly.com/question/11234923

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