TASK 1: Consider a simple experiment such as the roll of a pair of dice; the sam
ID: 3334720 • Letter: T
Question
TASK 1: Consider a simple experiment such as the roll of a pair of dice; the sample space is given belovw (11)(12 (31) (32) (33) (4) (35 (36) A)) 4) (4,4) (A5)46) Classical Probability Calculate the following probabilities: a) Find the probability of the first die being a 22 b) Which elements of the sample space satisfy this criterion? c) Find the probability of the sum of the pair of dice equaling seven. d) Which elements of the sample space satisfy this criterion? e) Find the probability that the second die is 2 more than the first die? f) Which elements of the sample space satisfy this criterion? 9) Find the probability that the dice sum to 7 and the second die is 2 more than the first, h) Which elements of sample space satisfy this criterion?Explanation / Answer
Solution:
( a )
the probability of first die being 2 = 6 / 36 = 0.166
( b )
the elements of the sample space satisfy this criteria are
( 2 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 )
( c )
the probabilty of sum of the pair of dies is 7 = 6 / 36 = 0.166
( d )
the elements in sample space that satisfy above criteria are
( 1 , 6 ) , ( 2 , 5 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1)
( e )
the probability that the second die is two more than the first die = 4 / 36 = 0.1111
( f )
the elements that satisfy this criteria are
( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 )
( g )
probability that the dies sum is 7 and the second die is 2 more than first die = 0 / 36 = 0
( h )
there are no elements in the sample space to satisfy the above critria
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