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Step-by-step explanation:

#3

P(A) = 3/8P(B) = 2/7

(i)

P(A and B) = P(A) * P(B) = 3/8*2/7 = 3/28

(ii)

P(A or B) = P(A) + P(B) - P(A and B) = 3/8 + 2/7 - 3/28 = 1/56(21 + 16 - 6) = 31/56

(iii)

P(not A and not B) = P(not A) * P(not B) = (1 - 3/8)*(1 - 2/7) = 5/8*5/7 = 25/56

Another way:

P(not A and not B) = 1 - P(A or B) = 1 - 31/56 = 25/56

#4

Outcomes with two fair coins: TT, TH, HT, HH

Outcomes with normal dice: 1 to 6

a)

P(odd number) = 3/6 = 1/2

b)

P(two heads and an even number) = 1/4*3/6 = 1/8

c)

P(head and tail) = 1/2P(prime) = 3/6 = 1/2 (primes are 2, 3 and 5)P(head, tail and prime) = 1/2*1/2 = 1/4

d)

P(two tails and odd number) = 1/4*3/6 = 1/8

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