obtain the probability distribution of the number of sixes in two tosses of a die
Answers
Answer:
Step-by-step explanation:
When a die is tossed up twice, we get 6 ×× 6 = 36 outcomes. Given that success is defined as any number greater than 4.
The sample space of the roll of the die is given by: S = ⎧⎩⎨⎪⎪⎪⎪⎪⎪1,12,13,14,15,16,11,2...............1,31,41,51,66,6⎫⎭⎬⎪⎪⎪⎪⎪⎪{1,11,21,31,41,51,62,1...3,1...4,1...5,1...6,1...6,6}
Let X be the random variable that defines the number of tosses where 6 appears on at least one die.
P (X = 0) = P (6 does not appear on either die) = ⎧⎩⎨⎪⎪⎪⎪1,12,13,14,15,11,2............1,31,41,55,5⎫⎭⎬⎪⎪⎪⎪{1,11,21,31,41,52,1...3,1...4,1...5,1...5,5} = 25362536
P (X = 1) = P (6 appears at least on one die) = {1,66,12,66,23,6,34,66,45,66,56,6}{1,62,63,4,65,66,66,16,26,36,46,5} = 11361136
Therefore the probability distribution is represented as follows: XP(X)0253611136