A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working ?

• 0.06

• 0.16

• 0.84

• 0.94

Three independent events, A₁, A₂, and A₃, occur with probabilities P(A_i) = $\frac{1}{1 + \mathrm{i}}$, i = 1, 2, 3. What is the probability that at least one of the three events occurs ?

• $\frac{1}{4}$

• $\frac{2}{3}$

• $\frac{3}{4}$

• $\frac{1}{24}$

Acoin is tossed three times. Consider the following events:

A : No head appears

B : Exactiy one head appears

C : At least two heads appear

Which one of the following is correct ?

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

• $\left(\mathrm{A} \cap \mathrm{B}\text{'}\right) \cup \left(\mathrm{A} \cap \mathrm{C}\text{'}\right) = \mathrm{B}\text{'} \cup \mathrm{C}\text{'}$

• $\mathrm{A} \cap \left(\mathrm{B}\text{'} \cup \mathrm{C}\text{'}\right) = \mathrm{A} \cup \mathrm{B} \cup \mathrm{C}$

• $\mathrm{A} \cap \left(\mathrm{B}\text{'} \cup \mathrm{C}\text{'}\right) = \mathrm{B}\text{'} \cap \mathrm{C}\text{'}$

84.

In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively.If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team Awill score 5 points in the series ?

• $\frac{17}{18}$

• $\frac{11}{12}$

• $\frac{1}{12}$

• $\frac{1}{18}$

Let the random variable X follow B(6. p). If 16 P(X = 4) = P(X = 2), then what is the value of P ?

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{1}{5}$

• $\frac{1}{6}$

If A = {x : 0 ≤ x ≤ 2} and B = {y; y is a prime number}, then what is A ∩ B equal to ?

• $\mathrm{\phi }$

• {1}

• {2}

• {1, 2}

In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what per cent of students play neither cricket nor football ?

• 10%

• 15%

• 20%

• 25%

If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes ?

• $\frac{5}{216}$

• $\frac{25}{216}$

• $\frac{125}{216}$

• $\frac{175}{216}$

Consider the following statements :

1) If A and B are mutually exclusive events, then it is possible that P(A) = P(B) = 0.6.

2) If A and B are any two events such that P (A/B) = 1, then. $\mathrm{P}\left(\raisebox{1ex}{$\overline{\mathrm{B}}$}\!\left/ \!\raisebox{-1ex}{$\overline{\mathrm{A}}$}\right.\right) = 1$

Which of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

There are 3 coins in a box. One is a two-headed coin; another is a fair coin; and third is biased coin that comes up heads 75% of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin ?

• $\frac{2}{9}$

• $\frac{1}{3}$

• $\frac{4}{9}$

• $\frac{5}{9}$