This is a classic example of "OR" and "AND" combination probability.

For a single roll of dice - Prob of getting a "1" is 1/6 and Prob of not getting a 1 is 5/6

Now the probability in question is "She gets a "1" in less than 3 rolls of dice" can be translated into

She gets the "1" in the first roll OR

She gets the "1" in the 2nd roll OR

She gets the "1" in the 3rd roll

Now, consider the first scenario - She gets "1" in the first roll - Probability= 1/6

Second scenario: She doesnt get the "1" in first roll AND gets the "1" in the second roll - Probabilty (5/6) * (1/6)

Third Scenario: She doesnt get "1" in first and second rolls AND gets it in the third roll-

Probability (5/6) * (5/6) * (1/6)

Since all three scenarios are independent of each other we add the 3 results

1/6 + [5/6 *1/6] + [ 5/6 * 5/6 * 1/6]

Hope that helps.

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Time to play the game...