First Naukri Probability Quiz -1

Reqd. Probability = 1 – (Vidit Gujrathi not winning even one Game out of 3) =1 - (1/3)2 = 1 - (1/9) = (8/9)

The probability that Raikonnen will pass Quali 2 = 1/2

So, the Probability that Raikonnen will fail Quali 2 = 1/2.

Probability that Giovinazzi will pass Quali 2 = 1/3

So, Probability that Giovinazzi will fail Quali 2 = 2/3.

Probability that both will pass in Quali 2 = Probability that Raikonnen will pass and probability that Giovinazzi will pass

= 1/2 x 1/3 = ⅙

Probability that only one person will pass is when Raikonnen passes and Giovinazzi fails or Raikonnen fails and Giovinazzi passes.

= (1/2) x (2/3) + (1/2) x (1/3) = ½

Probability that at least one person, will pass, so the possibilities

can be (Raikonnen pass and Giovinazzi fails), or (Raikonnen fails and Giovinazzi pass) or (Both Raikonnen and Giovinazzi pass)

(1/2) x (2/3) + (1/2) x (1/3) + (1/2) x (1/3) = ⅔

There are 13 diamonds. Three diamonds out of 13 diamonds can be taken out in ^{13}C_{3} ways.

Total number of sample spaces = ^{52}C_{3}

Required probability = \frac{^{13}C_{3}}{^{52}C_{3}}.

P (of dark chocolate in first attempt) = 6 / 14 = 3 / 7

Here probability will remain the same for the next two attempts.

Therefore, Required Probability = (3/7) x (3/7) x (3/7) = 27 / 343

Probability of getting business class tickets from bag I = 8 / 14

Probability of getting business class tickets from bag II = 7 / 12

Hence reqd. Prob. = (8/14) x (7/12) = (1/3)

It is given that the last three digits are randomly dialled. then each of the digits can be selected out of 10 digits in 10 ways.

Hence required probability =(\frac{1}{10})^{3}=\frac{1}{1000}

The probability that the chairperson will be an officer from theBlue Team is 

\frac{2}{3}\times\frac{3}{4}

and the probability that the chairperson will be an officer from the Red Team is

\frac{1}{3}\times\frac{2}{7}.

Therefore, (\frac{2}{3}\times\frac{3}{4}) + (\frac{1}{3}\times\frac{2}{7}) = \frac{25}{42}

Solution: They will contradict each other if:

David is true and Goliath is false \frac{3}{4}\times\frac{1}{6}

Or

David is false and Goliath is true \frac{1}{4}\times\frac{5}{6}

Therefore, (\frac{3}{4}\times\frac{1}{6}) + (\frac{1}{4}\times\frac{5}{6}) = \frac{1}{3}