What is the probability that Mark. Colleen. Jeff, and Emily win the first, secon

Question

What is the probability that Mark. Colleen. Jeff, and Emily win the first, second, third, and fourth prizes, respectively, in a drawing if 30 people enter a contest and no one can win more than one prize. winning more than one prize is allowed. To roll a total of 8. do you prefer two dice or three dice Justify your answer. Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits arc independent and if a 0 bit and a 1 bit are equally likely. the probability that a bit is a 1 is 0.7. the probability that the ith bit is a 1 is 1/2^i for i = 1, 2, 3.........10. Find the probability that a randomly generated bit string of length 10 begins with a 1 or ends with a 00 for the same conditions as in parts (a), (b), and (c) of (i), if bits are generated independently. Assume that the probability a child is a girl is 0.6 and that the sexes of children bum into a family are independent. What is the probability that a family of four children has exactly three girls at least one boy at least one girl all children of the same sex Let X be the product of the numbers that appear when a pair of dice is rolled. What arc the values of this random variable for all the possible outcomes when these two dice are rolled Suppose that Lea selects a ball by first picking one of two boxes at random and then selecting a ball from this box. The first box contains 4 red balls and 6 purple balls, and the second box contains 8 red balls and 10 purple balls. What is the probability that Lea picked a ball from the second box if she has selected a red ball Suppose that 5% of the patients tested in a clinic are infected with avian influenza. Furthermore, suppose that w hen a blood test for avian influenza is given. 98% of the patients infected with avian influenza test positive and that 2% of the patients not infected with avian influenza test positive. What is the probability that

Explanation / Answer

Hi below i have given solution for two questions for your reference, Sorry i couldn;t get the exact solution for the rest.

2.To roll a total of 8 , do you prefer two dice or three dice?

n(s)= 6^3= 216 when we roll 3 dice .

now getting 8 on the three dice

6 1 1 these three numbers can be arranged in 3!/2! ways= 3ways
5 2 1 these three numbers can be arranged in 3! = 6ways
4 2 2 these three numbers can be arranged in 3!/2!= 3 ways
4 3 1 these three numbers can be arranged in 3!= 6 ways
3 3 2 these three numbers can be arranged in 3!/2!= 3 ways

total no of ways = 3+6+3+6+3= 21 ways

so desired probability = 21/216.

4. Assume that the probability a child is a girl is 0.6 and that the sexes of children born into a family are independent. What is the probability that a family of four children has

a) exactly three girls?

b) at least one boy?

c) at least one girl?

d) all children of the same sex?

a) P(a) = C(4, 3) * (0.6)^3 * (1-0.6)^4-3
b) P(b) = 1 - P(All girls) = 1 - (1-0.6)^4
c) P(c) = 1 - P(All boys) = 1 - 0.6^4
d) P(d) = P(All girls) + P(All boys) = (1-0.6)^4 + 0.6^4

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