Question

Q. Three fair dice are rolled together at the same time. Find the probability that the product of the three numbers appearing on their tops is a prime number.

Answer 1

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♦♦ PRObabILITY ♦♦

→ Desired Event : Product of the Three Numbers is a Prime Number 

→ By definition, a prime number has only '1' and the no. itself as factors.

=> The dice must show up, two times '1' and one times a prime √√

=> Number of such events = ( 1 , 1 , { 2 , 3 , 5 } ) = 3 events
→ Hence, showing up of an a prime has ( 3 x 3 ) = 9 events

♦♦ Number of Possible Events = 6³ = 216

=> Probability = [ No. of events ÷ Total Possible Events ] = [ 9 / 216 ] 
                       = [ 1 / 24 ]

Answer 2

Hi ,

If Three fair dice are rolled ,

Let ' E ' be the event that the product of

the three numbers appearing on their

tops is a prime .

number of total possible

outcomes = 6³ = 216 -----( 1 )

favorable outcomes = { ( 1,1,2), ( 1,2,1),(2,1,1),(1,1,3),

(1,3,1),(3,1,1),(1,1,5),(1,5,1),(5,1,1)}

Therefore ,

number of outcomes favorable to E = 9 ---( 2 )

p( E ) = ( 2 ) / ( 1 )

= 9/216

= 1/24

I hope this helps you.

: )