12 1 point An undergraduate student believes that the probab

12. (1 point) An undergraduate student believes that the probability of getting an admission from graduate school A is 60 percent, and the probability that he gets an admission from graduate school B is 55 percent. Also he believes that the probability of getting admission from both schools is 35 percent. Calculate the probability that he will get admission at least from one of these schools? A) 0.45 B) 0.55 C) 0.6 D) 0.8

Solution

12.

P(A U B) = P(A) + P(B) - P(A n B)

=0.60 + 0.55 - 0.35

= 0.80 [ANSWER, D]

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13.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success =    0.4      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.070543872
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.929456128 [ANSWER, A]

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