If you throw a six sided die twice, what is the probability that you will get:
(i) A one on the first throw OR a two on the second throw ?
(ii) A one on the first toss AND a two on the second toss of the die ?
1) Either-or probabilities are found by adding the individual probabilities.
2) If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To calculate the probabilities, we need to understand the basic principles of probability.
In both cases, we will use the concept of probability as a ratio of the number of favorable outcomes to the total number of possible outcomes.
(i) To find the probability of getting a one on the first throw OR a two on the second throw, we need to find the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
- Getting a one on the first throw: 1 possibility
- Getting a two on the second throw: 1 possibility
Total possible outcomes:
When throwing a six-sided die twice, each throw has 6 possible outcomes. So, the total possible outcomes for two throws is 6 × 6 = 36.
Therefore, the probability of getting a one on the first throw OR a two on the second throw is: (1 + 1) / 36 = 2 / 36 = 1 / 18.
(ii) To find the probability of getting a one on the first toss AND a two on the second toss, we need to find the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
- Getting a one on the first throw: 1 possibility
- Getting a two on the second throw: 1 possibility
Total possible outcomes:
Similar to the previous case, the total possible outcomes are 6 × 6 = 36.
Therefore, the probability of getting a one on the first toss AND a two on the second toss is: (1 × 1) / 36 = 1 / 36.
In summary:
(i) Probability of getting a one on the first throw OR a two on the second throw: 1 / 18.
(ii) Probability of getting a one on the first toss AND a two on the second toss: 1 / 36.