Unsolved Probability Questions

The following questions are from arun sharma and no hint/solution is provided in the book
So Please explain how to solve them

Q1. A fair coin is tossed 10 times. Find the probability that two heads do not occur consecutively?
a. 1/2^4
a. 1/2^3
c. 1/2^5
d. None of these

Q2. The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that he will get both the contracts?
a. 19/45
b. 13/45
c. 12/35
d. 11/23

Q3. Three faces of a dice are yellow, two faces are red and one face is blue. The dice is tossed three times. Find the probability that the colors yellow, red and blue appear in first, second and third toss respectively.
a. 1/18
b. 1/12
c. 1/9
d. 1/36

Q4. A bag contain 15 tickets numbered 1 to 15. A ticket is drawn and replaced. Then one more ticket is drawn and replaced. The probability that first number drawn is even and second is odd is
a. 56/225
b. 26/578
c. 57/289
d. None of these

Thanks in advance

Q2. Use

Q2. Use P(A U B) = P(A) + P(B) - P(A ∩ B) =>Probability of getting both the contracts = 2/3 + 5/9 - 4/5 = 19/45

Q3. answer

Probability of getting yellow color = P(Y) = 3/6 = 1/2 Probability of getting red color = P(R) = 2/6 = 1/3 Probability of getting blue color = P(B) = 1/6 So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/6 = 1/32

Q4. Same as Q3.

Q4. Same as Q3. 7/15 x 8/15 = 56/225

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To anita1

To anita1 specifically 
1/6*1/3*1/2 is not 1/32
6*3*2=36
So the answer is 1/36 and not 1/32

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Great job! 
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for my problem used.