Tossing a coin 15 times find the probability of getting exac

Tossing a coin 15 times find the probability of getting exactly 4 tails. Find the probability of getting at least 4 talls for tossing a coin 15 times. An airliner wants to know the probability of on time flights for its flights 215 from Orlando to LA. It selects 20 flights randomly, If 92% of the flights are on time. Find the probability that exactly 6 flights are on time. Find the probability that at least 3 flights are on times. Find the probability that between 6 and 10 flights, inclusive, are on time. In a shipment of 40 bolts, 12 are defective, 20 bolts are picked at random. Assume all the bolts look alike and have equal probability of being chosen; what is the probability that all 20 are non-defective? A committee of 8 is selected at random from a group of faculty members consisting of 16 from the Mathematics Department, 20 from the Chemistry Department, and 15 from the English Department What is the probability that the committee will consist of 4 from the Mathematics Department and 4 from the Chemistry Department? What is the probability that the committee will consist of 3 from the Mathematics Department and 5 from the English Department? What is the probability that the committee will consist of 2 from the Mathematics Department, 2 from the Chemistry Department, and 4 from the English Department? Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find the probability that An employer has three positions to fill from a group of 17 applicants, eight men and 97 women. He selects at random from the applicants. What is the probability that two will be men and one will be a women? What is the probability that at least one woman is selected? A bridge hand consists of 13 cords dealt at random from a dock of 52. Calculate the probabilities of the following:

Solution

6.

a)

There are 4c2 ways to get 2 kings, 4 ways to get 1 queen, and 44C2 ways to get the other 2 cards.

There are 52C5 ways to get any 5 cards.

Thus,

P = (4C2)(4)(44C2)/(52C5) = 0.008735802 [ANSWER]

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b)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    52      
K = number of successes in the population =    13      
n = sample size =    5      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.274279712 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    52      
K = number of successes in the population =    13      
n = sample size =    5      
x = number of successes in the sample =    3      
          
Thus,          
          
P(   3   ) =    0.081542617 [ANSWER]

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d)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    52      
K = number of successes in the population =    26      
n = sample size =    5      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.025310124 [ANSWER]