Coin Tossing An unfair coin is tossed three times It is unfa

Coin Tossing.- An unfair coin is tossed three times. It is unfair since in each toss the chance of landing ft head is only 1/3. Thus all of the outcomes in the sample space are not equally likely Define two events as follows: Find the probability of event A. Are events A and D independent? Justify your answer..

Solution

9.

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.333333333      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.222222222 [ANSWER]

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B)

No. If they are independent, then P(A) = P(A|B).

However, given B, it makes A impossible, that is, P(A|B) = 0, because you need 4 tosses to have that.

Thus, THEY ARE NOT INDEPENDENT.

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