If 5 of a Company’s 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection, then what is the probability that none of the trucks chosen meet emission standards ?

• $\frac{1}{8}$

• $\frac{3}{8}$

• $\frac{1}{12}$

• $\frac{1}{4}$

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is a prime number ?

• $\frac{5}{12}$

• $\frac{1}{2}$

• $\frac{7}{12}$

• $\frac{2}{3}$

If a coin is tossed till the first head appears, then what will be the sample space ?

• {H}

• {TH}

• {T, HT, HHT, HHHT, ...}

• {H, TH, TTH, TTTH, ...}

A bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective ?

• 0.0087

• 0.016

• 0.026

• 0.047

A coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails ?

• 0.16

• 0.48

• 0.58

• 0.98

If $\mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = \frac{5}{6}, \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{3} \mathrm{and} \mathrm{P}\left(\overline{\mathrm{A}}\right) = \frac{1}{2}$ then which one of the following is not correct ?

• $\mathrm{P}\left(\mathrm{B}\right) = \frac{2}{3}$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \mathrm{P}\left(\mathrm{A}\right)\mathrm{P}\left(\mathrm{B}\right)$

• $\mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) > \mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right)$

• $\mathrm{P}\left(\overline{\mathrm{A}} \cap \overline{\mathrm{B}}\right) = \mathrm{P}\left(\overline{\mathrm{A}}\right)\mathrm{P}\left(\overline{\mathrm{B}}\right)$

If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6 ?

• $\frac{5}{6}$

• $\frac{5}{9}$

• $\frac{1}{2}$

• $\frac{5}{12}$

Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02, 0.03 and 0.05, it fails to rise. In the restaurant where they work, X bakes 50%, Y bakes 30% and Z bakes 20% of cakes. What is the probobility of failures caused by X ?

• $\frac{9}{29}$

• $\frac{10}{29}$

• $\frac{19}{29}$

• $\frac{28}{29}$

If A and B are two events such that P(A) = 0.6, P(B) = 0.5 and P(A∩B) = 0.4, then consider the following statements :

$$\begin{gathered} 1. \mathrm{P}\left(\overline{\mathrm{A}} \cup \mathrm{B}\right) = 0.9 \\ 2. \mathrm{P}\left(\overline{\mathrm{B}} \mathrm{U} \overline{\mathrm{A}}\right) = 0.6 \end{gathered}$$

Which of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

•  Neither 1 nor 2

Consider a random variable X which follows Binomial distribution with parameters n = 10 and $\mathrm{p} = \frac{1}{5}$ Then Y = 10 –X follows Binomial distribution with parameters n and p respectively given by

• 5, $\frac{1}{5}$

• 5, $\frac{2}{5}$

• 10, $\frac{3}{5}$

• $10, \frac{4}{5}$