12 + Interview Questions in PROBABILITY DISTRIBUTION IN GENERAL AWARENESS Page 1 InterviewSolution

1.	State the relation between the probability of success and failure in Bernoulli trials.
Answer» The relation between the probability of success and failure in Bernoulli trials is p + q = 1.

Discussion

2.	Find the standard deviation of the binomial distribution having n = 8 and probability of failure
Answer» n = 8, q = 23 ∴ p = 1 – q = 1 – \(\frac{2}{3} = \frac{1}{3}\) Standard deviation of the binomial distribution: √npq = \(\sqrt{8\times\frac{1}{3}\times\frac{2}{3}}=\sqrt{\frac{16}{9}}=\frac{4}{3}\) Hence, the standard deviation of the binomial distribution obtained is \(\frac{4}{3}\).

2.

Find the standard deviation of the binomial distribution having n = 8 and probability of failure

Answer»

n = 8, q = 23

∴ p = 1 – q = 1 – \(\frac{2}{3} = \frac{1}{3}\)

Standard deviation of the binomial distribution:

√npq = \(\sqrt{8\times\frac{1}{3}\times\frac{2}{3}}=\sqrt{\frac{16}{9}}=\frac{4}{3}\)

Hence, the standard deviation of the binomial distribution obtained is \(\frac{4}{3}\).

Discussion

3.	The probability of failure in a binomial distribution is 0.6 and the number of trials in it is 5. Find the probability of success.
Answer» The probability of failure q = 0.6, n = 5 S The probability of success p = 1 – q = 1 – 0.6 = 0.4

3.

The probability of failure in a binomial distribution is 0.6 and the number of trials in it is 5. Find the probability of success.

Answer»

The probability of failure q = 0.6, n = 5

S The probability of success p = 1 – q

= 1 – 0.6
= 0.4

Discussion

4.	The binomial distribution has mean 5 and variance \(\frac{10}{7}\). What will be the type of this distribution ?(a) Positively skewed(b) Negatively skewed(c) Symmetric(d) Nothing can be said about the distribution
Answer» Correct option is (b) Negatively skewed

Discussion

5.	Define continuous random variable.
Answer» If a random variable X is an element of R or its subset, whose interval is (a, b),

Discussion

6.	Which of the following is the formula of probability of an event of not getting a success in the binomial distribution with parameters n and p?(a) nC0pnq0(b) nC0p0qn(c) nC0pqn(d) nC0pnq
Answer» Correct option is (b) ⁿC₀p⁰q_n

Discussion

7.	Define discrete random variable.
Answer» A random variable X, which is capable of assuming all the values, in set of real numbers or its subsets, is called a discrete random variable. Examples of a discrete random variable are: number of children per family, getting number of heads when a coin is tossed three times.

Discussion

8.	Which variable of the following will be an illustration of discrete variable ?(a) Height of a student(b) Weight of a student(c) Blood Pressure of a student(d) Birth year of a student
Answer» Correct option is (d) Birth year of a student

Discussion

9.	State the formula to find variance of discrete variable.
Answer» The formula to find the variance of discrete variable is as follows : σ² = V(X) = E(X²) – [E(X)]² = Σx²p (x) – [Σx ∙ p(x)]²

9.

State the formula to find variance of discrete variable.

Answer»

The formula to find the variance of discrete variable is as follows :

σ² = V(X) = E(X²) – [E(X)]²
= Σx²p (x) – [Σx ∙ p(x)]²

Discussion

10.	Mean and variance of a discrete probability distribution are 3 and 7 respectively. What will be E (X2) for this distribution ?(a) 10(b) 4(c) 40(d) 16
Answer» Correct option is (d) 16

Discussion

11.	If the probability that any 50 year old person will die within a year is 0.01, find the probability that out of a group of 5 such persons(i) none of them will die within a year(ii) at least one of them will die within a year.
Answer» p = Probability that any 50 year old person will die within a year = 0.01 ∴ q = 1 – p = 1 – 0.01 = 0.99 X is binomial random variable. ∴ Putting, n = 5, p = 0.01, q = 0.99 in P(X = x) = p(x) = ⁿC_xp^xq^n-x P(X = x) = p(x) = ⁵C_x(0.01)^x(0.99)^n-x (i) None of the 50 year old person will die within a year, i.e., X = 0 ∴ P(X = 0) = p(0) = ⁵C₀(0.01)⁰ (0.99)^5-0 = 1 × 1 × (0.99)⁵ = 0.9510 (ii) At least one of them will die within a year, i.e., X ≥ 1 Now, P(X ≥ 1) = p(1) + p (2) + p(3) + p( 4) + p (5) = 1 – p(0) = 1 – 0.9510 = 0.049

11.

If the probability that any 50 year old person will die within a year is 0.01, find the probability that out of a group of 5 such persons(i) none of them will die within a year(ii) at least one of them will die within a year.

Answer»

p = Probability that any 50 year old person will die within a year = 0.01

∴ q = 1 – p = 1 – 0.01 = 0.99
X is binomial random variable.

∴ Putting, n = 5, p = 0.01, q = 0.99 in
P(X = x) = p(x) = ⁿC_xp^xq^n-x
P(X = x) = p(x) = ⁵C_x(0.01)^x(0.99)^n-x

(i) None of the 50 year old person will die within a year, i.e.,
X = 0
∴ P(X = 0) = p(0) = ⁵C₀(0.01)⁰ (0.99)^5-0
= 1 × 1 × (0.99)⁵
= 0.9510

(ii) At least one of them will die within a year, i.e., X ≥ 1
Now, P(X ≥ 1)
= p(1) + p (2) + p(3) + p( 4) + p (5)
= 1 – p(0)
= 1 – 0.9510
= 0.049

Discussion

12.	The probability that a bomb dropped from a plane over a bridge will hit the bridge is \(\frac{1}{5}\). Two bombs are enough to destroy the bridge. If 6 bombs are dropped on the bridge, find the probability that the bridge will be destroyed.
Answer» p = Probability that a bomb dropped over a bridge = \(\frac{1}{5}\) = 0.2 X is binomial random variable. ∴ P(x = x) = p(x) = ⁿC_xp^xq^n-x Putting, n = 6, p = \(\frac{1}{5}\) = 0.2, q = \(\frac{4}{5}\) = 0.8 P(X = x) = p(X) = ⁶C_x(0.2)^x(0.8)^6-x Two bombs are enough to destroy the bridge. i.e., X ≥ 2 ∴ P(X ≥ 2) = 1 – p[X ≤ 1] = 1 – [p(0) + p(1)] ………… (1) ∴ p(0) = ⁶C₀(0.2)⁰(0.8)⁶ = 1 × 1 × 0.2621 = 0.2621 ∴ p(1) = ⁶C₁(0.2)¹(0.8)⁵ = 6 × 0.2 × 0.32768 = 0.3932 Putting the values of p(0) and p(1) in the result (1), P[X ≥ 2] = 1 – [0.2621 + 0.3932] = 1 – 0.6553 = 0.3447 Hence, the probability that the bridge will be destroyed obtained is 0.3447.

12.

The probability that a bomb dropped from a plane over a bridge will hit the bridge is \(\frac{1}{5}\). Two bombs are enough to destroy the bridge. If 6 bombs are dropped on the bridge, find the probability that the bridge will be destroyed.

Answer»

p = Probability that a bomb dropped over a bridge = \(\frac{1}{5}\) = 0.2
X is binomial random variable.

∴ P(x = x) = p(x) = ⁿC_xp^xq^n-x

Putting, n = 6, p = \(\frac{1}{5}\) = 0.2, q = \(\frac{4}{5}\) = 0.8

P(X = x) = p(X) = ⁶C_x(0.2)^x(0.8)^6-x

Two bombs are enough to destroy the bridge. i.e., X ≥ 2

∴ P(X ≥ 2) = 1 – p[X ≤ 1]

= 1 – [p(0) + p(1)] ………… (1)

∴ p(0) = ⁶C₀(0.2)⁰(0.8)⁶

= 1 × 1 × 0.2621 = 0.2621

∴ p(1) = ⁶C₁(0.2)¹(0.8)⁵

= 6 × 0.2 × 0.32768

= 0.3932

Putting the values of p(0) and p(1) in the result (1),

P[X ≥ 2] = 1 – [0.2621 + 0.3932]

= 1 – 0.6553

= 0.3447

Hence, the probability that the bridge will be destroyed obtained is 0.3447.

Discussion

Explore topic-wise InterviewSolutions in .

State the relation between the probability of success and failure in Bernoulli trials.

Find the standard deviation of the binomial distribution having n = 8 and probability of failure

The probability of failure in a binomial distribution is 0.6 and the number of trials in it is 5. Find the probability of success.

The binomial distribution has mean 5 and variance \(\frac{10}{7}\). What will be the type of this distribution ?(a) Positively skewed(b) Negatively skewed(c) Symmetric(d) Nothing can be said about the distribution

Define continuous random variable.

Which of the following is the formula of probability of an event of not getting a success in the binomial distribution with parameters n and p?(a) nC0pnq0(b) nC0p0qn(c) nC0pqn(d) nC0pnq

Define discrete random variable.

Which variable of the following will be an illustration of discrete variable ?(a) Height of a student(b) Weight of a student(c) Blood Pressure of a student(d) Birth year of a student

State the formula to find variance of discrete variable.

Mean and variance of a discrete probability distribution are 3 and 7 respectively. What will be E (X2) for this distribution ?(a) 10(b) 4(c) 40(d) 16

If the probability that any 50 year old person will die within a year is 0.01, find the probability that out of a group of 5 such persons(i) none of them will die within a year(ii) at least one of them will die within a year.

The probability that a bomb dropped from a plane over a bridge will hit the bridge is \(\frac{1}{5}\). Two bombs are enough to destroy the bridge. If 6 bombs are dropped on the bridge, find the probability that the bridge will be destroyed.