Binomial Distribution

Q.

A fair coin is tossed a fixed number of items. If the probability of getting$7$ heads is equal to that of getting $9$ heads, then the probability of getting $3$ heads is

1. $\frac{35}{2^{12}}$

2. $\frac{35}{2^{14}}$

3. $\frac{7}{2^{12}}$

4. None of these

Q. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

1. 1/4
2. 3/8
3. 1/2
4. 3/4

Q.

A die is thrown three times.

Getting a $3$ or a $6$ is considered a success.

Then the probability of at least two successes is

1. $\frac{2}{9}$

2. $\frac{7}{27}$

3. $\frac{1}{27}$

4. None of these

Q.

A dice is thrown $5$ times then the probability that an even number will come up exactly $3$ times is

1. $\frac{5}{16}$

2. $\frac{1}{2}$

3. $\frac{3}{16}$

4. $\frac{3}{2}$

Q.

A coin is tossed twice. The probability of getting head both the times is

1. $\frac{1}{2}$

2. $\frac{1}{4}$

3. $\frac{3}{4}$

4. $1$

Q. The probability of a defective piece being produced in a manufacturing proces is 0.01. The probability that out of 5 successive pieces, only one is defective, is

1. $\left(0.99{)}^4\right(0.01)$
2. $\left(0.99\right)(0.01{)}^4$
3. $5\times \left(0.99\right)(0.01{)}^4$
4. $5\times \left(0.99{)}^4\right(0.01)$

Q.

Consider an unbiased cubic dice with opposite faces coloured identically an each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is

1. 0.2593

Q.

Let in a Binomial distribution, consisting of$5$ independent trials, probabilities of exactly $1$ and$2$ successes be$0.4096$ and $0.2048$ respectively. Then the probability of getting exactly $3$ successes is equal to:

1. $80/243$

2. $32/625$

3. $128/625$

4. $40/243$

Q. If a fair coin is tossed 4 times, what is the probability that two heads and two tails will result?

1. $\frac{3}{8}$
2. $\frac{1}{2}$
3. $\frac{5}{8}$
4. $\frac{3}{4}$

Q.

The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is .

1. 0.41

Q. The probability of obtaining at least two 'Six' in throwing a fair dice 4 times is

1. 425/432
2. 19/144
3. 13/144
4. 125/432

Q. A six-faced fair dice is rolled five times. The probability (in %) of obtaining "ONE" at least four times is

1. 33.3
2. 3.33
3. 0.33
4. 0.0033

Q. In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively

1. 90 and 9
2. 9 and 90
3. 81 and 90
4. 9 and 81

Q. A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

1. $\frac{1}{6}$
2. $\frac{3}{8}$
3. $\frac{1}{8}$
4. $\frac{1}{2}$

Q. An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is

1. 1/9
2. 1/8
3. 2/3
4. 3/8

Q. Let X be the Poisson random variable with parameter $\lambda =1$, then the probability $P(0\le x\le 2)$ equals

1. $\frac{1}{2e}$
2. $\frac{3}{2e}$
3. $\frac{5}{2e}$
4. $\frac{7}{2e}$

Q.

A coin is tossed $5$ times. Find the probability of getting at least $4$ heads

Q. A lot had 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

1. 0.0036
2. 0.1937
3. 0.2234
4. 0.3874

Q. If 20 percent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats is

1. 0.2048
2. 0.4000
3. 0.4096
4. 0.9421

Q. The probability that a thermistor randomly picked up from a produced unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is

1. 0.001
2. 0.057
3. 0.107
4. 0.3

Q.

A die is rolled $5$ times. What is the probability that $1$ occurs twice, and $2,3$ and $4$ occur once each, and $5$ and $6$ do not occur (round off to fourth decimal place).

Q. Shaquille O' Neal is a 60% career free throw shoots, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

1. 0.2508
2. 0.2816
3. 0.2934
4. 0.6000