Theoretical Probability

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What is theoretical probability?

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Theoretical probability is the likelihood of an event happening based on all possible outcomes, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

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How do you calculate the probability of rolling a specific sum with two dice?

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To calculate the probability of rolling a specific sum with two dice, count the number of combinations that result in that sum and divide by the total number of combinations (36).

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What is the probability of rolling a sum of 4 with two dice?

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The probability is 1/12, as there are 3 combinations (1+3, 2+2, 3+1) that result in a sum of 4 out of 36 total combinations.

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What is the probability of picking a specific color sock from a drawer?

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The probability is calculated by dividing the number of socks of that color by the total number of socks.

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If there are 6 white, 4 black, and 2 brown socks, what is the probability of picking a brown sock first and then a black sock?

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The probability is 1/18, calculated as (2/12) * (4/12) after replacing the first sock.

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What is the probability of rolling a 4 on a die?

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The probability is 1/6, as there is one favorable outcome (rolling a 4) out of 6 possible outcomes.

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What is the probability of rolling a number less than 3 after rolling a 4?

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The probability is 1/3, as there are 2 favorable outcomes (1 and 2) out of 6 possible outcomes.

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What is the probability of flipping a coin 3 times and getting 3 heads?

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The probability is 1/8, as there is only 1 favorable outcome (HHH) out of 8 possible outcomes (2^3).

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What is the total number of outcomes when rolling two dice?

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The total number of outcomes when rolling two dice is 36, as each die has 6 faces (6 x 6 = 36).

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What is the probability of picking a brown cow first and then a white cow from a farm with 5 brown and 10 white cows?

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The probability is 5/21, calculated as (5/15) * (10/14) after one cow is removed.