A biased die is such that P(4)`=1/10` and other scores being equally likely. The die tossed twice. If X is the number of four seen, then find the variance of the random variable X.

Explanation

To solve the problem step-by-step, we will find the probabilities associated with the random variable \( X \), which represents the number of times a 4 is rolled when a biased die is tossed twice. The probability of rolling a 4 is given as \( P(4) = \frac{1}{10} \), and since the die is biased, the remaining outcomes (1, 2, 3, 5, 6) must have equal probabilities.

### Step 1: Determine the Probability of Not Rolling a 4
Since the total probability must equal 1, we can find the probability of not rolling a 4:

\[ P(\text{not } 4) = 1 - P(4) = 1 - \frac{1}{10} = \frac{9}{10} \]
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