probability

The definition of a prime no. is it cannot be factorised into two natural numbers (except 0 and 1).

So, if a prime number can be formed by a product of two nos. (1, 2, 3, 4, 5, 6), one of them must be 1.

actually, there are only 3 possible prime nos., which are 2, 3, 5

The possible combination are:

1x2=2 or 2x1=2
1x3=3 or 3x1=3
1x5=5 or 5x1=5

Pr (the product of two toss is a prime no.) = 6/36 = 1/6

However, if the first toss is an odd no. (1, 3, 5), the combinations become:

1x2=2
1x3=3 or 3x1=3
1x5=5 or 5x1=5

Pr (the product of two toss is a prime no., given that the first toss is an odd no.)
= 5 / (3 x 6) = 5 / 18

1.Two fair dice are tossed.

(a) Find the probability that the product is a prime number.
[Solution: prime number are: 2, 3, 5. Product is a prime number: (1,2),(2,1),(1,3),(3,1),(1,5),(5,1)]

Answer(a):
P( product is a prime number ):
= [( 1 / 6 ) ( 1 / 6 ) ] x 6
= ( 1 / 36 ) 6
= 1 / 6

∴The probability that the product is a prime number is 1 / 6.
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2.A fair dice is tossed twice. If the first toss is an odd number, what is the probability that the sum of the two tosses is 7?
[Solution: an odd number + the second tossed number = 7=P[(1,6),(3,5),(5,2)]

Answer(2):
P( sum of the two tosses is 7 ):
=[ ( 1 / 6 ) ( 1 / 6 ) ] x 3
=( 1 / 36 ) 3
= 1 / 12

∴ The probability that the sum of the two tosses is 7 is 1 / 12.
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