A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge on the rectangle

• $\frac{2}{3}$

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{2}{5}$

A fair coin is tossed l00 times. What is the probability of getting tails an odd number of times ?

• $\frac{1}{2}$

• $\frac{3}{8}$

• $\frac{1}{4}$

• $\frac{1}{8}$

What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets

• 60

• 120

• 500

• 1000

A special dice with numbers 1, - 1, 2, - 2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero ?

• $\frac{1}{72}$

• $\frac{1}{8}$

• $\frac{7}{72}$

• $\frac{25}{216}$

There is 25% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days ?

• $1 - {\left(\frac{1}{4}\right)}^7$

• ${\left(\frac{1}{4}\right)}^7$

• ${\left(\frac{3}{4}\right)}^7$

• $1 - {\left(\frac{3}{4}\right)}^7$

A salesman has a 70% chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B ?

• 0.98

• 0.91

• 0.70

• 0.49

A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, II  or all the three. The probabilities of the student passing in tests I, II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2, then which one of the following is correct ?

• m(1 + n) = 1

• n(1 + m) = 1

• m = 1

• mn = 1

Three candidates solve a question. Odds in favour of the correct answer are 5 : 2, 4 : 3 and 3 : 4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly ?

• $\frac{209}{343}$

• $\frac{134}{343}$

• $\frac{149}{343}$

• $\frac{60}{343}$

79.

A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine ?

• $\frac{1}{1024}$

• $\frac{243}{1024}$

• $\frac{1023}{1024}$

• $\frac{781}{1024}$

for two events, A and B, it is given that P(A) = $\frac{3}{5}$, P(B) = $\frac{3}{10}$and P$\left(\mathrm{A}\overline{)\mathrm{B}}\right) = \frac{2}{3}$. If $\overline{\mathrm{A}} \mathrm{and} \overline{\mathrm{B}}$ are the complementary events of A and B, then what is $\mathrm{P}\left(\overline{\mathrm{A}} \overline{) \overline{\mathrm{B}}}\right)$ = ?

• $\frac{3}{7}$

• $\frac{3}{4}$

• $\frac{1}{3}$

• $\frac{4}{7}$