Question

Two fair dice are rolled simultaneously. It is found that one of them shows odd prime numbers the probabilty that the remaining dice also shows

Answer 1

in a dice there are total 6 out comes, 1,2,3,4,5&6. now among them odd primes are 3&5.so the probability to get odd prime on second dice is 2/6 =1/3

Answer 2

As per the data given in the above question.

We have to find the probability of odd prime number on both dice .

Given,

Two dice rolled simultaneously

Step-by-step explanation:

The sample of Two fair dice rolled simultaneously

Total outcomes is 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].

• Let event A or P(A)= one of the dice show odd prime number, and
• Let event B or P(B)= remaining dice also shows odd prime number.

Now,

The following outcomes shows that one dice must show odd prime number .

$(3, 1), (1, 3) (3, 2), (2, 3) (3, 3), \\ (3, 4) (4, 3), (3, 5) (5, 3), (3, 6) \\ (6, 3), (5, 1), (1, 5), (5, 2), (2, 5), \\ (5, 4), (4, 5), (5, 5), (5, 6), (6, 5).$

Our of total 36 we find that 20 outcomes shows the odd prime probability condition.

• we know that ,Odd prime on a die are 3 and 5.

But both shows the probability is 4

$A⋂B= (3,3),(5,5),(3,5),(5,3)$

$P (odd \: prime)= \frac{Favourable \: outcomes}{Total \: outcomes }$

So,

Favourable outcome= 4

Total outcomes =20

$P(odd prime )= \frac{4}{20}$

$P(odd prime )= \frac{1}{5}$

Hence,

Both dice show odd prime number probability is 1/5.

Project code #SPJ3