Question on Probability and Independent Events

 Question on Probability and Independent Events

 

 

 

Question on Probability

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Find the probability of not getting a sum of 7 or 11

total on either of the two toss of a pair of fair dice .

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Answer

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The sample space of total events from the throw of the

two dice consists of 36 pairs of dice throw events

 

So , a probability of 1/36 is given to each event's

Occurrence .

 

Let A be the event of getting a 7 or 11 on

the throw of two dices

= {1,6} , {2,5} ,{3,4} ,{4,3} ,{5,2} , {6,1} ,{5,6} ,{6,5}

So , probability of occurrence of event A

=P(A)

= 8/36

= 2/9

 

So , the probability of not getting a 7 or 11 on the throw

of both the dice are

= P(A')

= 1 - 2/9

=7/9

 

Let A1 be event of first throw

Let A2 be the event of second throw

The probability of getting a sum of 7 or 11 on the first and

second throw of the dices are

P(A1')* P(A2')

= (7/9) *(7/9)

= 49/81