In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 - p. The probability of answering a question correctly is $\frac{1}{\mathrm{m}}$, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is :

• $\frac{\mathrm{mp}}{1 + \mathrm{mp}}$

• $\frac{\mathrm{mp}}{1 + (\mathrm{m} - 1)\mathrm{p}}$

• $\frac{\left(\mathrm{m} - 1\right)\mathrm{p}}{1 + \left(\mathrm{m} - 1\right)\mathrm{p}}$

• $\frac{\left(\mathrm{m} - 1\right)\mathrm{p}}{1 +\hspace{0.17em}\mathrm{mp}}$

Five sticks of length 1, 3,5, 7 and 9 feet are given.Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle ? 

• 0.5

• 0.4

• 0.3

• 0

Three dice are thrown simultaneously. What is the probability that the sum on the three faces is atleast 5 ?

• $\frac{17}{18}$

• $\frac{53}{54}$

• $\frac{103}{108}$

• $\frac{215}{216}$

Two independent events A and B have P(A)= $\frac{1}{3}$ and P(B) = $\frac{3}{4}$· What is the probability that exactly one of the two events A or B occurs ?

• $\frac{1}{4}$

• $\frac{5}{6}$

• $\frac{5}{12}$

• $\frac{7}{12}$

A coin is tossed three times. What is the probability of getting head and tail alternately ?

• $\frac{1}{8}$

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{3}{4}$

A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade ?

• $\frac{1}{52}$

• $\frac{1}{13}$

• $\frac{1}{4}$

• $\frac{1}{8}$

If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4 ?

• $\frac{13}{18}$

• $\frac{5}{6}$

• $\frac{11}{12}$

• $\frac{35}{36}$

What is the probability of 5 Sundays in the month of December ?

• $\frac{1}{7}$

• $\frac{2}{7}$

• $\frac{3}{7}$

• None of the above

A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit ?

• 5

• 6

• 7

• None of the above

For two mutually exclusive events A and B, P(A) =0.2 and P($\overline{\mathrm{A}} \cap \mathrm{B}$) = 0.3. What is $\mathrm{P}\left(\overline{)\mathrm{A}}\left(\mathrm{A} \cup \mathrm{B}\right)\right)$ equal to

• $\frac{1}{2}$

• $\frac{2}{5}$

• $\frac{2}{7}$

• $\frac{2}{3}$