Question

Five dice are thrown simultaneously .If the occurrence of an even number in a single die is considered as a success find the probability of at most 3 successes

Answer 1

Answer:

There are $^5C_3\cdot 3^3\cdot 3^2+^5C_2\cdot 3^2\cdot 3^3+^5C_1\cdot 3\cdot 3^4+3^5$=6318 ways of getting 0,1,2 or 3 successes.

Let event X be the number of even-numbered dices obtained

∴ Pr(X≤3)=$\frac{\left(^5C_3\cdot 3^3\cdot 3^2+^5C_2\cdot 3^2\cdot 3^3+^5C_1\cdot 3\cdot 3^4+3^5\right)}{6^5}=\frac{13}{16}$

I think this is right.

Hope this helps :)

Step-by-step explanation: