Question

if two dice are thrown and two numbers are chosen at random, then find the probability of getting
1)both the number are prime
2)both the number are even.
my maths exam is going on. please help. don't cheat ​

Answer 1

Answer:

When two dice are thrown we get outcome as

[ (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) ]

Therefore sample space is equal to 36

Now prime no. between 1–6 are 2, 3 and 5 and favorable outcome on both dices will be

[ (2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5) ]

it means that favorable outcome is 9

Now probability = total favorable outcome/ sample space

that is 9/36

= 1/4 or 0.25

Hence probability of getting a prime number on both dice is1/4

she wants to say:

Best of luck for exam