The probability that a student will answer one question correctly is p=51⇒q=54 .
Using Bernoulli's formula, we find the probabilities that a student will correctly answer 10, 11, 12, 13, 14 and 15 questions, respectively:
P(10)=C1510p10q5=10!5!15!⋅(51)10⋅(54)5=305175781253075072
P(11)=C1511p11q4=11!4!15!⋅(51)11⋅(54)4=610351562569888
P(12)=C1512p12q3=12!3!15!⋅(51)12⋅(54)3=61035156255824
P(13)=C1513p13q2=13!2!15!⋅(51)13⋅(54)2=6103515625336
P(14)=C1514p14q=14!1!15!⋅(51)14⋅(54)=610351562512
P(15)=p15=(51)15=305175781251
Then the wanted probability is
P(x≥10)=P(10)+P(11)+P(12)+P(13)+P(14)+P(15)=305175781253075072+610351562569888+61035156255824+6103515625336+610351562512+305175781251=305175781253455373
Answer: P(x≥10)=305175781253455373
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