Question

What is the probability that the product of the numbers is a multiple of 7 ?

Hint:

Instead of checking all 12 products, identify the key condition. A product is a multiple of 7 if at least one factor is a multiple of 7. Only Box 1 contains a multiple of 7 (the number 7 itself). The probability of picking 7 from Box 1 is 1/4. The number from Box 2 doesn't matter (probability is 3/3 = 1). The combined probability is (1)/(4) × 1 = (1)/(4).

Answer 1

Using the same setup as the previous question, we now need to find the probability that the product of the two numbers drawn is a multiple of 7.
Box 1: 1, 3, 5, 7
Box 2: 2, 4, 6
P(Event) = Number of favorable outcomesTotal number of possible outcomes Total number of possible outcomes:
As before, the total number of possible pairs is 4 × 3 = 12.

Number of favorable outcomes:
For the product of two numbers to be a multiple of 7, at least one of the numbers must be a multiple of 7.
In Box 1, the number 7 is present.
In Box 2, there are no multiples of 7.
Therefore, a favorable outcome occurs only when we draw the number 7 from Box 1. The number drawn from Box 2 can be any of its three numbers (2, 4, or 6).
The favorable pairs are:
(7, 2) → Product = 14 (Multiple of 7)
(7, 4) → Product = 28 (Multiple of 7)
(7, 6) → Product = 42 (Multiple of 7)
There are 3 favorable outcomes.

Calculating the probability:
P(product is a multiple of 7) = Favorable outcomesTotal outcomes = (3)/(12) Simplifying the fraction:
P(product is a multiple of 7) = (1)/(4) The probability that the product is a multiple of 7 is (1)/(4).