a true or false test has 5 questions. what is the probability of guessing exactly four out of the five answers correstly.
damn you guys been eating since 2009
Pr(4/5)= 1/2*1/2*1/2*1/2*1/2
remember, guessing exactly 4 right is guessing the last one wrong also.
damn you guys been cheating since 2009
To calculate the probability, we need to know the total number of possible outcomes and the number of favorable outcomes.
In this scenario, there are 2 possible outcomes for each question: a correct answer or an incorrect answer. Since it's a true or false test, the probability of guessing correctly is 1/2, or 0.5.
To find the number of favorable outcomes - guessing exactly four out of the five questions correctly - we can use the combination formula.
The formula for calculating combinations is:
C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen.
For our case, n = 5 (total questions) and r = 4 (number of questions guessed correctly).
C(5, 4) = 5! / (4!(5-4)!)
= 5! / (4! * 1!)
= 5
So, there are 5 favorable outcomes (guessing exactly four out of the five questions correctly).
Now, let's calculate the total number of possible outcomes. Since each question has 2 possible answers (true or false) and there are 5 questions in total:
Total number of possible outcomes = 2 * 2 * 2 * 2 * 2 = 2^5 = 32
Therefore, the probability of guessing exactly four out of the five answers correctly is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 5 / 32
= 0.15625
So, the probability is approximately 0.15625, or 15.625%.