if a die is tossed four times what is the probability of getting three odd numbers
1/2 on each toss, right?
yes
To find the probability of getting three odd numbers when a die is tossed four times, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When a fair six-sided die is tossed, the total number of outcomes is 6 for each toss. Since we are tossing the die four times, the total number of outcomes can be calculated as 6 * 6 * 6 * 6 = 1296.
Number of Favorable Outcomes:
For each toss, the favorable outcomes are when the result is an odd number, which is 3, since the odd numbers on a die are 1, 3, and 5. Therefore, the number of favorable outcomes for each toss is 3.
To calculate the number of favorable outcomes when tossing the die four times, we need to determine the number of ways to select 3 out of the 4 tosses to obtain odd numbers. This can be calculated using the binomial coefficient:
C(4,3) = 4! / (3! * (4-3)!) = 4
Hence, there are four ways to select three out of the four tosses to result in odd numbers.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= (Number of favorable outcomes for each toss)^(Number of favorable outcomes)
/ (Total number of outcomes)^(Number of tosses)
= (3^3 * 4) / 6^4
= 108 / 1296
= 9 / 108
= 1 / 12
Therefore, the probability of getting three odd numbers when a die is tossed four times is equal to 1/12.