Ask Question
7 September, 19:42

Someone rolls a six sided fair die 5 times. They consider it a success if they have a two or three on a die. Whats the probability of 2 successes? no successes? and at least 3 successes?

+4
Answers (1)
  1. 7 September, 20:23
    0
    2 successes = 80/243

    0 successes = 32/243

    at least 3 successes = 51/243

    Step-by-step explanation:

    Lets suppose we had the following sequence of 5 throws:-

    2 or 3, 2 or 3, then NOT 2 or 3 on last 3 throws

    Probability of this is

    1/3 * 1/3 * 2/3 * 2/3 * 2/3 = 8/243

    There are (5*4) / 2 = 10 ways of having this result (that is the number of combinations of 2 from 5 = 5C2).

    So Prob (2 successes) = (8/243) * 10 = 80/243

    Prob (No successes) = (2/3) ^5 = 32/243

    Probability of 3 successes = 1/3 * 1/3 * 1/3 * 2/3 * 2/3 * 5C3

    4/243 * 10 = 40 / 243

    Probability of 4 successes = (1/3) ^4 * 2/3 * 5C4

    = 10/243

    Probability of 5 success = (1/3) ^5 = 1 / 243

    Prob (at least 3 successes) = 51/243
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Someone rolls a six sided fair die 5 times. They consider it a success if they have a two or three on a die. Whats the probability of 2 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers