in throwing two dice find the probability ofcoming even number on both probability of coming odd number on dice probability of different number on both dice
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
both even number = 3/6 * 3/6 = ?
both odd = same
different = 1/6 * 5/6 = ?
To find the probabilities of different outcomes when throwing two dice, we need to find the total number of possible outcomes and then count the number of favorable outcomes for each scenario.
1. Probability of getting an even number on both dice:
To find this probability, we need to determine the number of favorable outcomes where both dice show an even number.
Total number of outcomes when throwing two dice: There are 6 possible outcomes for each die (numbers 1 to 6), so the total number of outcomes for two dice is 6 * 6 = 36.
Number of favorable outcomes: Out of the 36 possible outcomes, there are 9 outcomes where both dice show an even number (2, 4, or 6). These favorable outcomes are: (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), and (6, 6).
Probability = Number of favorable outcomes / Total number of outcomes
Probability of getting an even number on both dice = 9/36 = 1/4 = 25%
2. Probability of getting an odd number on the dice:
Similarly, we need to count the number of favorable outcomes where at least one die shows an odd number.
Number of favorable outcomes: Out of the 36 possible outcomes, there are 27 outcomes where at least one die shows an odd number. These favorable outcomes are all outcomes except for the 9 outcomes mentioned earlier where both dice show even numbers.
Probability of coming an odd number on at least one die = Number of favorable outcomes / Total number of outcomes
Probability of getting an odd number on the dice = 27/36 = 3/4 = 75%
3. Probability of getting different numbers on both dice:
The probability of getting different numbers on both dice is the complement of getting the same number. To find this probability, we need to count the number of favorable outcomes where both dice show different numbers.
Number of favorable outcomes: There are 6 * 5 = 30 favorable outcomes where both dice show different numbers. For each number on the first die, there are 5 possible outcomes on the second die that are different.
Probability of getting different numbers on both dice = Number of favorable outcomes / Total number of outcomes
Probability of getting different numbers on both dice = 30/36 = 5/6 = 83.33%