The binomial expression 8C2 (1/3)^2(2/3)^6 gives the probability
A.At least 2 successes in 8 trials of the probability of success is 1/3
B.At least 2 successes in 8 trials of the probability of success in one trial 2/3
C.Exactly 2 successes in 8 trials of the probability of success is 1/3
Would it be c? Would it be exact or at least?
c, exactly two successes
Well, let's take a closer look at the binomial expression 8C2 (1/3)^2(2/3)^6.
The expression 8C2 represents the combination of choosing 2 successes out of 8 trials.
Then we have (1/3)^2, which represents the probability of success (1/3) occurring exactly 2 times.
Finally, we have (2/3)^6, which represents the probability of failure (2/3) occurring 6 times.
So, all put together, the expression gives us the probability of having exactly 2 successes and 6 failures in 8 trials where the probability of success is 1/3.
Therefore, the correct answer is C. It represents the probability of exactly 2 successes in 8 trials.
The given binomial expression 8C2 (1/3)^2(2/3)^6 gives the probability of exactly 2 successes in 8 trials, where the probability of success is 1/3 in each trial.
Therefore, the correct answer is C.
To determine whether the answer is "exact" or "at least," we can break down the given binomial expression and interpret it.
The binomial expression 8C2 represents the number of ways to choose 2 successes out of 8 trials. It can be calculated using the formula:
nCr = n! / (r!(n-r)!)
where n represents the total number of trials and r represents the desired number of successes. In this case, we have 8C2, which is calculated as:
8C2 = 8! / (2!(8-2)!) = 8! / (2!6!) = (8 * 7) / (2 * 1) = 28.
Now, let's break down the rest of the expression:
(1/3)^2 represents the probability of success (1/3) occurring exactly 2 times in the trials.
(2/3)^6 represents the probability of failure (2/3) occurring exactly 6 times in the trials.
Multiplying these three components together, we get:
8C2 (1/3)^2 (2/3)^6 = 28 * (1/3)^2 * (2/3)^6.
Therefore, the expression represents the probability of exactly 2 successes (each with a probability of 1/3) and 6 failures (each with a probability of 2/3) occurring among 8 trials.
So the answer to your question is indeed C. This expression gives the probability of exactly 2 successes in 8 trials, where the probability of success in each trial is 1/3.