the probability that when three dice are rolled at the same time, the largest value of three number rolled is 4. Let A be the outcome in which the largest number is 4, B be the outcome in which the largest number is 4 or less, and Let C be the outcome in which the largest number is 3 or less. P(B) =?

Question

anonymous · Answer

the sample space contains 216 events. to calculate the probability that the largest no. is 4 or less, we have to add the probabilities that the largest no. is 1, the largest no. is 2, the largest no. is 3 ans the largest no. is 4.
now P(largest no. is 1)=P(1,1,1)=1/216
P(the largest no. is 2)= P[(1,1,2),(1,2,1),(1,2,2),(2,1,1),(2,1,2),(2,2,1),(2,2,2)]=7/216.
similarly calculate P(the largest no. is 3) and P(the largest no. is 4) and add them all.

anonymous · Answer

i dont understand why the sample space contain 216, please explaind to me?

anonymous · Answer

its because every dice can take 6 values. so the total sample space contains 6*6*6 = 216

anonymous · Answer

on the problem, 1 dice, the largest number is 4, not 6 isnt it? so i think the sample space is 4, maybe... CMIIW

anonymous · Answer

oh sorry i understood the question now. give me a few minutes to reply back

anonymous · Answer

oke, thanks before..

anonymous · Answer

the first line is quite ambiguous. does it mean that the experiment has already taken place and the largest no. obtained is 4? why is it even there? the first sentence is not complete.