A multiple choice quiz has 10 questions each with four alternatives.

Question

A multiple choice quiz has 10 questions each with four alternatives. A
passing score is 6 or more correct. If a student attempts to guess the correct answer to each
question what is the probability that he passes?

 

could you please help me with that how can I find the probability ?

Answer 1

The probability of getting multiple questions correct is found by determining the probability of getting the individual questions correct and multiplying them together. 

 

EX: probability of flipping tails twice in a row is 1/2 * 1/2 = 1/4

 

This question is not quite that simple because it asks the probability of "passing," i.e. getting "at least" 6 correct. So we need to find the probability of getting 6 right, 7 right, 8 right, 9 right, and 10 right, then add those together.

 

P(6 correct): 1/4 * 1/4 * 1/4 * 1/4 * 1/4 * 1/4 = (1/4)⁶ = 1/4,096

 

P(7 correct):  (1/4)⁷ = 1/16,384

 

P(8 correct):  (1/4)⁸ = 1/65,536

 

P(9 correct):  (1/4)⁹ = 1/262,144

 

P(10 correct): (1/4)¹⁰ = 1/1,048,576

 

Σ = 341/1,048,576