What is the probability of getting at least two questions correct by guessing?
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This is a probability question, so let's what is taught in the class to solve it!!
There are four questions, and each guess of right answer is 1/2 and 1/2 for wrong.
To guess it right for at least 2 questions means there are three conditions:
2 are correct, 3 are corrects, and 4 all correct.
For 2 correct:
It is 4C2 (denotes out of any four questions, pick any two to guess them right!)
so the probability is [1/2 * 1/2] * [(1 - 1/2)(1 - 1/2)]
the first two are assume they are guessed right, then the last two are for the wrong. Then you time the combination of possible configuration, 4C2,
[1/2 * 1/2] * [(1 - 1/2)(1 - 1/2)] * 4C2 = 1/16 * 6 = 6/16
for 3 correct, 4C3:
the probability is [1/2 * 1/2 * 1/2] * [(1 - 1/2)]
the first three are assume they are guessed right, then the last one are for the wrong. Then you time the combination of possible configuration, 4C3,
[1/2 * 1/2 * 1/2] * [(1 - 1/2)] * 4C3 = 1/16 * 4 = 4/16
and 4 all correct, 4C3:
the probability is [1/2 * 1/2 * 1/2 * 1/2]
all four are guessed right. Then you time the combination of possible configuration, 4C4,
[1/2 * 1/2 * 1/2 * 1/2] * 4C4 = 1/16 * 1 = 1/16
all together, you have 1/16 + 4/16 + 6/16 = 11/16
There are four questions, and each guess of right answer is 1/2 and 1/2 for wrong.
To guess it right for at least 2 questions means there are three conditions:
2 are correct, 3 are corrects, and 4 all correct.
For 2 correct:
It is 4C2 (denotes out of any four questions, pick any two to guess them right!)
so the probability is [1/2 * 1/2] * [(1 - 1/2)(1 - 1/2)]
the first two are assume they are guessed right, then the last two are for the wrong. Then you time the combination of possible configuration, 4C2,
[1/2 * 1/2] * [(1 - 1/2)(1 - 1/2)] * 4C2 = 1/16 * 6 = 6/16
for 3 correct, 4C3:
the probability is [1/2 * 1/2 * 1/2] * [(1 - 1/2)]
the first three are assume they are guessed right, then the last one are for the wrong. Then you time the combination of possible configuration, 4C3,
[1/2 * 1/2 * 1/2] * [(1 - 1/2)] * 4C3 = 1/16 * 4 = 4/16
and 4 all correct, 4C3:
the probability is [1/2 * 1/2 * 1/2 * 1/2]
all four are guessed right. Then you time the combination of possible configuration, 4C4,
[1/2 * 1/2 * 1/2 * 1/2] * 4C4 = 1/16 * 1 = 1/16
all together, you have 1/16 + 4/16 + 6/16 = 11/16
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Because each question has 2 possible answers, the chances are split from a 100% chance to a 50% chance of getting the question right. if there are two questions, each having a 50-50 chance of being correct by guessing, that means that the first problem has a 1/2 chance of being correct, and the 2nd problem also has a 1/2 chance of being correct. to find the possibility of getting both those answers correct, you multiply the fractions together. 1/2 chance x 1/2 chance = 1/4 chance because 1/2x1/2=1/4. There is a 1/4 chance of getting AT LEAST 2 problems correct by guessing. If you are trying for exactly 2 problems, the math is slightly different.