1. Some event does not happen in three observations with the probability of 0.21

Question

1. Some event does not happen in three observations with the probability of 0.216. Seven independent observations are made. Calculate the probability that the event happened exactly four times. 2. 15 students are trying to pass the exam that consists of 20 question cards and each student is required to answer one of them chosen at random. 5 students know answers to 15 question cards and aren't able to answer the rest 5; three students did not put enough effort into preparation and know answers to only 10 question cards; the other students know answers to all question cards. What is the probability that a student chosen at random from these 15 students will not pass the exam, if the probability to pass the exam is 0.98 if the student knows the answer to the question cards he/she gets and 0 otherwise?

Explanation / Answer

QUestion 1

Pr(Success of event happening) = p

so here

Pr(no event in 3 events) = (1 - p)3 = 0.216

so,

1- p = 0.6

p = 0.4

Pr(X = 4 ; 7 ; 0.4) = 7C4 (0.4)4 (0.6)3 = 0.1935

Question 2

Here for 5 students, probability of getting a known question= 15/20 = 3/4

for 3 students, probability of getting a known question = 10/20 = 1/2

for rest 8 students,probability of getting a known question = 1

Pr(a random person chosen will fail the exam) = 1* (1 - 3/4) * (5/15) + (1 - 0.98) * (1 - 1/2) * 3/15) + (1 - 0.98) * 8/15

= 0.096

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