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BCA Semester 3 – Probability and Statistics – Unit 4: Probability (8Hrs)

Comprehensive questions and detailed answers for Unit 4: Probability (8Hrs). Perfect for exam preparation and concept clarity.

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Fit a Binomial Distribution from the following data where $p = 0.5$ :

\begin{array}{|c|c|c|c|c|} \hline \text{No. of heads} & 1 & 2 & 3 & 4 \\ \hline \text{Frequency} & 28 & 62 & 20 & 4 \\ \hline \end{array}

MediumTHEORY5 marks2019(TU FOHSS Final)

Given a normal distribution with mean $=200$ and standard deviation $=20$ , find the probability that:

\begin{aligned} \text{i)}\ & P(X > 180) \\ \text{ii)}\ & P(X < 220) \\ \text{iii)}\ & P(160 < X < 240) \\ \text{iv)}\ & P(X > 220) \end{aligned}

Also, $10\%$ of the values are less than what value of $X$ ?

MediumTHEORY10 marks2019(TU FOHSS Final)

A box contains $50$ items of which $20$ are defective. If one item is selected randomly from the box, what is the probability that it is a non-defective item?

MediumTHEORY5 marks2020(TU FOHSS Final)

In a normal distribution with mean $=200$ and standard deviation $=20$ , find the probability that:

\begin{aligned} \text{i)}\ & P(X > 180) \\ \text{ii)}\ & P(X < 220) \\ \text{iii)}\ & P(160 < X < 240) \\ \text{iv)}\ & P(X > 220) \\ \text{v)}\ & 10\% \text{ values are less than what value of } X? \end{aligned}

MediumTHEORY10 marks2020(TU FOHSS Final)

Fit a Poisson distribution of the following data and calculate the expected frequencies:

\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline f & 56 & 156 & 132 & 92 & 37 & 22 & 4 & 0 & 1 \\ \hline \end{array}

MediumTHEORY5 marks2021(TU FOHSS Final)

A box contains 30 items of which 10 are defectives. If two items are selected randomly from the box without replacement, what is the probability that
$\quad \quad$ (a) both are defective
$\quad \quad$ (b) both are non‑defective?

MediumTHEORY5 marks2021(TU FOHSS Final)

The lifetime of a certain electronic component is a normal random variate with an expectation of 5000 hours and a standard deviation of 100 hours. Compute the probabilities under the following conditions:

\begin{aligned} (a)\ & P(\text{lifetime} < 3012) \\ (b)\ & P(4000 < \text{lifetime} < 6000) \\ (c)\ & P(\text{lifetime} < 4500) \\ (d)\ & P(\text{lifetime} > 7000) \end{aligned}

MediumTHEORY10 marks2021(TU FOHSS Final)

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Sample Questions

Fit a Binomial Distribution from the following data where $p = 0.5$: \[ \begin{array}{|c|c|c|c|c|} \hline \text{No. of heads} & 1 & 2 & 3 & 4 \\ \hline \text{Frequency} & 28 & 62 & 20 & 4 \\ \hline \e

Marks: 5Chapter: Unit 4: Probability (8Hrs)

Given a normal distribution with mean $=200$ and standard deviation $=20$, find the probability that: \[ \begin{aligned} \text{i)}\ & P(X > 180) \\ \text{ii)}\ & P(X < 220) \\ \text{iii)}\ & P(160 < X

Marks: 10Chapter: Unit 4: Probability (8Hrs)

A box contains $50$ items of which $20$ are defective. If one item is selected randomly from the box, what is the probability that it is a non-defective item?

Marks: 5Chapter: Unit 4: Probability (8Hrs)

In a normal distribution with mean $=200$ and standard deviation $=20$, find the probability that: \[ \begin{aligned} \text{i)}\ & P(X > 180) \\ \text{ii)}\ & P(X < 220) \\ \text{iii)}\ & P(160 < X <

Marks: 10Chapter: Unit 4: Probability (8Hrs)

Fit a Poisson distribution of the following data and calculate the expected frequencies: \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline f & 56 & 156 & 1

Marks: 5Chapter: Unit 4: Probability (8Hrs)

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