Question

A box contains four slips numbered 1, 3, 5, 7 and another box contains three slips numbered 2, 4, 6. If one slip is drawn from each box.
(i). What is the probability that the product of the numbers being a prime ?

Hint:

For a product of two integers to be prime, one of the integers must be 1 and the other must be a prime number. In this problem, we need to pick 1 from the first box and a prime number (2, 4, 6) from the second. The only prime in the second box is 2. So the only favorable pair is (1, 2). This logic helps find the answer quickly.

Answer 1

We are drawing one number from each of two boxes and finding the product. We need to calculate the probability that this product is a prime number.
Box 1: 1, 3, 5, 7
Box 2: 2, 4, 6
P(Event) = Number of favorable outcomesTotal number of possible outcomes We need to list all possible pairs and their products to find the favorable and total outcomes.

Total number of possible outcomes:
There are 4 choices from Box 1 and 3 choices from Box 2.
Total number of pairs = 4 × 3 = 12.
The possible pairs (Box1, Box2) are:
(1,2), (1,4), (1,6)
(3,2), (3,4), (3,6)
(5,2), (5,4), (5,6)
(7,2), (7,4), (7,6)
Number of favorable outcomes:
We need to find the product for each pair and check if it is a prime number. (A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself).
Products:
1 × 2 = 2 (Prime)
1 × 4 = 4 (Not prime)
1 × 6 = 6 (Not prime)
3 × 2 = 6 (Not prime)
3 × 4 = 12 (Not prime)
3 × 6 = 18 (Not prime)
5 × 2 = 10 (Not prime)
5 × 4 = 20 (Not prime)
5 × 6 = 30 (Not prime)
7 × 2 = 14 (Not prime)
7 × 4 = 28 (Not prime)
7 × 6 = 42 (Not prime)
The only product that is a prime number is 2, which comes from the pair (1, 2).
So, there is only 1 favorable outcome.

Calculating the probability:
P(product is prime) = (1)/(12) The probability that the product is a prime number is (1)/(12).