Two different dice are tossed together find the probability that the product of the two numbers

Two dice are rolled together, the possible outcomes is n(S) =n=6*6=36E be event of getting 2 number whose product is 6E=( 1,6),(2,3),(3,2),(6,1),n(E)=4

Probability of success p(E) =m/n=4/36=1/9

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Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25. 

Let us first write the all possible oucomes when Peter throws two different dice together.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

∴ Total number of outcomes = 36

The favorable outcome for getting the product of numbers on the dice equal to 25 is (5, 5).

Favourable number of outcomes = 1

∴ Probability that Peter gets the product of numbers as 25
=

The outcomes when Rina throws a die are 1, 2, 3, 4, 5, 6.

∴ Total number of outcomes = 6

Rina throws a die and squares the number, so to get the number 25, the favourable outcome is 5.

Favourable number of outcomes = 1

∴ Probability that Rina gets the square of the number as 25 

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Two different dice are tossed together, Find the probability that the product of the two numbers on the top of the dice is 6.

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Two dice are tossed

S = [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2), 4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]

Total number of outcomes when two dice are tossed = 6 x 6= 36

Favourable events of getting the product as 6 are:

(1 x 6 = 6), (6 x 1 = 6),(2 x 3 = 6),(3 x 2 = 6)

i.e.(1,6), (6,1), (2,3), (3,2)

Favourable events of getting product as 6 = 4

P(getting product as 6) = `4/36`

                                  = `1/9`

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Two different dice are tossed together.Find the probability that the product of two numbers on the top of the dice is 6 .

Solution

When two dice are thrown simultaneously,all possible outcomes are :

S=$\left[\begin{array}{c}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right]$

Total number of all outcomes=$6\times 6=36$

Favourable outcomes of getting the product as 6 are: (2,3),(3,2),(1,6),(6,1) Hence, number of favourable outcomes getting product as 6 is 4. Probability that the product of the two numbers on the top of the die is 6

$=\frac{4}{36}$

$=\frac{1}{9}$