231.

A fair coin is tossed n times. If the probability of getting 7 heads is equal to the probability of getting 9 heads, then the value of n will be

• 8

• 13

• 15

• None of these

The probabilities of solving a question by three students
are $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}$ respectively. What is the probability that the question is solved ?

• $\frac{35}{48}$

• $\frac{1}{48}$

• $\frac{11}{16}$

• $\frac{2}{11}$

A and B are two independent events. Probability of happening of both A and B is 1/6 and probability of happening of neither of them is 1/3, then the probability of events A and B are respectively

• $\frac{1}{2} \mathrm{and} \frac{1}{3}$

• $\frac{1}{5} \mathrm{and} \frac{1}{6}$

• $\frac{1}{2} \mathrm{and} \frac{1}{6}$

• $\frac{2}{3} \mathrm{and} \frac{1}{4}$

If m things are distributed among a men and b women. Then, the chance that the number of things received by men is odd, is

• $\frac{{\left(\mathrm{b} - \hspace{0.17em}\mathrm{a}\right)}^{\mathrm{m}} - {\left(\mathrm{b} + \mathrm{a}\right)}^{\mathrm{m}}}{2{\left(\mathrm{b} + \mathrm{a}\right)}^{\mathrm{m}}}$

• $\frac{{\left(\mathrm{b} + \hspace{0.17em}\mathrm{a}\right)}^{\mathrm{m}} - {\left(\mathrm{b} - \mathrm{a}\right)}^{\mathrm{m}}}{2{\left(\mathrm{b} + \mathrm{a}\right)}^{\mathrm{m}}}$

• $\frac{{\left(\mathrm{b} + \hspace{0.17em}\mathrm{a}\right)}^{\mathrm{m}} - {\left(\mathrm{b} - \mathrm{a}\right)}^{\mathrm{m}}}{{\left(\mathrm{b} + \mathrm{a}\right)}^{\mathrm{m}}}$

• None of these

If 0 < P(A) < 1, 0 < P(B) < 1 and P(A $\cup$ B) = P(A) + P(B) - P(A)P(B),then

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

• P(A/B) = P(A)

• Both (a) and (b) are  true

• None of the above

Find the binomial probability distribution whose mean is 3 and variance is 2.

• ${\left(\frac{2}{3} + \frac{1}{3}\right)}^9$

• ${\left(\frac{5}{3} + \frac{2}{3}\right)}^9$

• ${\left(\frac{3}{3} + \frac{1}{2}\right)}^9$

• None of these

For a binominal variate X, if n = 4 and P(X = 4) = 6P(X = 2), then the value of p is

• $\frac{3}{7}$

• $\frac{4}{7}$

• $\frac{6}{7}$

• $\frac{5}{7}$

In binomial distribution the probability of getting success is $\frac{1}{4}$ and the standard deviation is 3. Then, its mean is

• 6

• 8

• 10

• 12

If the mean of a poisson distribution is $\frac{1}{2}$, then the ratio of P(X = 3) to P(X = 2) is

• 1 : 2

• 1 : 4

• 1 : 6

• 1 : 8

A random variable X takes the values 0, 1 and 2. If P(X = 1) = P(X = 2) and P(X = 0) = 0.4, then the mean of the random variable X is

• 0.2

• 0.7

• 0.5

• 0.9