Sarvesh K Verma Solutions for Chapter: Probability, Exercise 4: Introductory Exercise

A bag contains $4$ red and $3$ black balls. A second bag contains $2$ red and $4$ black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

In a toys making factory, machine $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ manufacture respectively $25\%,35\%$ and $40\%$ of the total toys. Of their output $5\%,4\%$ and $2\%$ respectively are defective toys. A toy is drawn at random from the product. What is the probability that the toy drawn is defective?

A box contains $20$ bulbs. The probability that the box contains exactly $2$ defective bulbs is $0.4$ and the probability that the box contains exactly $3$ defective bulbs is $0.6$. Bulbs are drawn at random one by one without replacement and tested till the defective bulbs are found. What is the probability that the testing procedure ends at the twelfth testing?

In a toys making factory, machines $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ manufacture respectively $25\%,35\%$ and $40\%$ of the total toys of their output $5\%,4\%$ and $2\%$ respectively are defective toys. A toy is drawn at random from the product. If the toy drawn is found to be defective, what is the probability that it is manufactured by the machine $\mathrm{B}$?

An architecture company built $200$ bridges $400$ hospitals and $600$ hotels. The probability of damage due to earthquake of a bridge, hospital and hotel is $0.01,0.03$ and $0.15$ respectively. One of the construction gets damaged with earthquake. What is the probability that it is a bridge?

There are $3$ boxes each containing $3$ red and $5$ green balls. Also there are $2$ boxes, each containing $4$ red and $2$ green balls. A green ball is selected at random. Find the probability that this green ball is from a box of the first group.

A man speaks truth $3$ out of $4$ times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

A card from a pack of $52$ cards is lost. From the remaining cards of pack, two cards are drawn and are found to be diamonds. Find the probability of the missing card to be diamond.