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Four fair dice are thrown simultaneously. If the probability that the highest number obtained is 4 is `(25a)/1296` then 'a' is equal to ______.

#### Options

5.00

6.00

7.00

8.00

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#### Solution

Four fair dice are thrown simultaneously. If the probability that the highest number obtained is 4 is `(25a)/1296` then 'a' is equal to **7.00**.

**Explanation:**

4 must be obtained on at least one die. x = the number of dice on which 4 is obtained required probability and The rest of the numbers same from 1, 2, 3.

= `P_((x = 1)) + P_((x = 2)) + P_((x = 3)) + P_((x = 4))`

= `(""^4C_1 xx 3 xx 3 xx 3)/6^4 + (""^4C_2 xx 3^2)/6^4 + (""^4C_3. 3)/6^4 + 1/6^4`

= `(25 xx 7)/1296`

= `175/1296`

Now, `(25a)/1296 = (25 xx 7)/1296`

or a = 7

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