**Topic**

A box has 5 cards of the same type, each card has one of the numbers 1, 2, 3, 4, 5; Two different cards have two different numbers. Randomly draw a card from the box, record the number of the card drawn and return the card to the box. Consider the “Random draw 3 cards in a row” test.

Calculate the probability of event A: “The product of the numbers on the card in 3 draws is even”

**Solution method – See details**

The probability of event A being a number, symbol \(P\left( A \right)\) is determined by the formula: \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}}\), where \(n\left( A \right)\) and \(n\left( \Omega \right)\) denote the number of elements of set A and \(\Omega \) respectively.

The opposite event of event A is the non-occurring event A, denoted by \(\overline A \) and \(P\left( {\overline A } \right) + P\left( A \right) = first\)

**Detailed explanation**

+ Draw 3 consecutive test cards from 5 cards \( \Rightarrow n\left( \Omega \right) = 5.5.5 = 125\)

+ Consider the event for \(\overline A \): “The product of the numbers recorded on the card in 3 draws is odd” is the opposite event of the event A \( \Rightarrow n\left( {\overline A } \ right) = 3.3.3 = 27\)

\( \Rightarrow P\left( A \right) = 1 – P\left( {\overline A } \right) = 1 – \frac{{n\left( {\overline A } \right)}}{{ n\left( \Omega \right)}} = 1 – \frac{{27}}{{125}} = \frac{{98}}{{125}}\)