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Re: Given two fair dice, what is the probability that the sum of their no. [#permalink]

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10 Sep 2015, 19:09

1

This post was BOOKMARKED

This is my take on the question:

There are 10 ways in which you can get exactly one 3 when you throw the die. (1,3),(2,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)

Out of the 10 outcomes only 2 i.e. (1,3) and (3,1) are the possible outcomes of the event (sum=4)

Therefore the the probability that the sum of the numbers is 4 given that exactly one dice shows a 3 is 2/10 or 1/5

If the question had specified that "atleast one dice shows a 3" then the total number of outcomes would have been 11 since we would include (3,3) resulting in a probability of 2/11

This question can be solved using the method of conditional probability You do not need the formula once you get the hang of the concept.....I will mention it anyway

P(A|B) = Probability of event A occurring such that event B has already occurred = P(A & B) / P(B)

Here, event A is getting a sum of 4 we'll have 3 possibilities : (1,3), (2,2), (3,1)

Event B => one of the 2 dices already shows a 3 [NOTE : there is NO restriction on the other dice => both dices CAN throw a 3] we'll have 11 possibilities : (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6) So, P(B) = 11/36

Event A & B occurring => 2 possibilities => (1,3) & (3,1) So, P(A & B) = 2/36

Why u have considered (3,3) only once when i am throwing the dice 2 times. I have thrown (first trail-ft) the two dice i got (3ft,3ft) (1st die 3 and 2nd die 3). In next case (Second trail-st) i got (3st,3st) (1st die 3 on second trail and 2nd die 3 on second trail)

Why would you take (3,3) twice? The overall sample space (N=36) when 2 die are thrown is given by (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) ............................ (3,1) (3,2) (3,3)..................... (4,1) ................(4,4)............ (5,1)........................(5,5)..... (6,1)................................(6,6)

Understand this ---- all these possibilities (1,1) (2,2).....& so on will appear only once ..... these are unique possibilities Take this to be an equivalent of rectangular coordinates in 2D Coordinate Geometry

Re: Given two fair dice, what is the probability that the sum of their no. [#permalink]

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16 Oct 2017, 12:12

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