8. You toss two 12-sided dice and record the sum of the two faces facing up. If

Question

8. You toss two 12-sided dice and record the sum of the two faces facing up.
If you repeat this experiment 10 times, what is the probability the sum is 3 in the 5 times out of the 10 trials? The answer is 0.068, but why? 8. You toss two 12-sided dice and record the sum of the two faces facing up.
If you repeat this experiment 10 times, what is the probability the sum is 3 in the 5 times out of the 10 trials? The answer is 0.068, but why? 8. You toss two 12-sided dice and record the sum of the two faces facing up.
If you repeat this experiment 10 times, what is the probability the sum is 3 in the 5 times out of the 10 trials? The answer is 0.068, but why?

Explanation / Answer

For a 12 sided dice there are 12 possible outcomes from 1 to 12

For two dice total number of outcomes = 12*12 =144

Out of these total number of outcomes when some is 3 = 3 {(1,1),(1,2),(2,1)}

Thus, Probability of getting sum of 3 on a trial = 3/144 = 0.0208

Then we can consider this as binomial for our calculation with n=10,x=5,p=3/144,q=141/144

Required probability = 10C5*(3/144)5*(141/144)5

= 8.90*10^-7

= 0.00000089

Please note that probability of getting sum 3 in a single roll is 3/144 = 0.0208 which is very small so if we consider 5 out of 10 trails should result in that probability varu is extremely small

Note: This is the required probability(0.00000089) conidering 12 sided die

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