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

Academic Mathematics NCERT Class 10

Given: Two different dice are tossed together.

To do: To find the probability of the product of two numbers on the top of the dice is 6.

Solution:

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 possiblen outcomes when two dice are tossed$=6\times6$

Events of getting product as$( 6)=( 1,\ 6),\ ( 2,\ 3),\ ( 3,\ 2),\ ( 6,\ 1)$

Number of favourbalble outcomes$=6$

Probability of getting product as $( 6)=\frac{Number\ of\ possible\ outcomes}{Total\ nuumber\ of\ possible\ outcomes}$

$=\frac{6}{36}$

$=\frac{1}{6}$

Therefore the probability of getting a product of 6 as a result when two dice are rolled is $\frac{1}{6}$.

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Updated on: 10-Oct-2022

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