Question

Two dice are thrown at the same time. Find the probability of getting (a) same no. on the both side (b) different

no. on both dices.​

Answer 1

Answer:

A) 1/6

B) 5/6

Step-by-step explanation:

When two dice are thrown, the total number of possible outcomes is 36.

i.e., No of observation {(1,1),(1,2),(1,3).......(5,6),(6,6) =36

1. Favourable outcomes = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

No of event =6

We know that Probability = no. of events / no. of sample space

Required Probability  = 6/36=1/6

2.There are two ways to find the robability.

i.  Required probability = 1 - P(getting same number on both the dice)

= 1-1/6 = 5/6

ii.  Favourable outcomes are {(1,2),(1,3)......(6,5)}

No of events = 30

So, Required Probability = 30/36

= 5/6

Answer 2

The given question is Two dice are thrown at the same time

we have to find the probability of getting

(a) same no. on the both side

(b) different no. on both dices.

If two dices are thrown at the same time then the number of possible outcomes will be the sample space n(s) .

n(s) =36.

(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)

(a) The probability of getting the same number on both sides

the events are A=(1, 1) (2, 2) (3, 3) (4, 4), (5, 5), (6, 6)

no of events n(A) =6.

P(A) =

$\frac{n(a)}{n(s)}$

The probability is

$\frac{6}{36} = \frac{1}{6}$

(b) the probability of getting different number on both sides

=Total number of samples or probability - probability of samples getting the same number.

$= 1 - ( \frac{1}{6} )$

$= \frac{(6 - 1)}{6} = \frac{5}{6}$

The probability of getting the different number on both sides is

$\frac{5}{6}$

Probability of getting same numbers is

$\frac{6}{36}$

Probability of getting different numbers is

$\frac{30}{36}$

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