Out of random() and randint(), which function should we use to generate random numbers between 1 and 5. Justify.

If 5 positive integers are taken at random and multiplied together, the probability that the last digit of the product is 2, 4, 6, or 8 is:

$\frac{4^5 - 2^5}{5^5}$

4 out of 15 apples are rotten. They are taken out one by one at random and examined. The ones which are examined are not replaced. What is the probability that the 9th one examined is the last rotten one?

A $\frac{{ }^{4} C_{3} \times{ }^{11} C_{5}}{{ }^{15} C_{3}} \times \frac{1}{{ }^{7} C_{1}}$

B $\frac{{ }^{11} C_{5} \times{ }^{4} C_{4}}{{ }^{15} C_{9}}$

C $\frac{{ }^{4} C_{3} \times{ }^{11} C_{5}}{{ }^{15} C_{9}}$

D none of these

An item is manufactured by three machines A, B, and C. Out of the total number of items manufactured during a specified period, 50% are manufactured on A, 30% on B, and 20% on C. 2% of the items produced on A and 2% of items produced on B are defective, and 3% of those produced on C are defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine A?

Four positive integers are taken at random and multiplied together. The probability that the product ends in an odd digit other than 5 is:

A $\frac{609}{625}$

B $\frac{16}{625}$

C $\frac{2}{5}$

D $\frac{1}{5}$

• (A): Increasing the number of observations minimizes random errors.
• (R): Positive and negative random errors occur with equal probability.

Both (A) and (R) are true and (R) is the correct explanation of (A).