Question

Find the probability of throwing a sum of 7 at least 9 times in 11 throws
of a pair of fair dice.

Answer 1

As we know that on throwing a pair of dice together then we will get total 36 outcomes

so we have to find the probability of getting sum of numbers on dices equal to 7

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

Hence total number of possible outcomes =x=6

now

P(getting sum of 7 in single throw of pair of fair dice ) =p=6/36 =1/6

now let X is number of times we get sum equal to 7 when we throw a pair of dice 11 times

Hence X~ Bin (11,1/6) so

now we have to find P(X>9)

now