Answer:
Probability that the product is an odd number = [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
Given - Patryk has 7 cards. There is a number on each card. 2 3 4 5 6 7 8
Patryk takes two of the cards at random. He works out the product
of the numbers on the two cards.
To find - Work out the probability that the product is an odd number.
Proof -
As we know that Product of two numbers is odd iff both the numbers are odd.
So, we have to find the probabilty that both the card that Patryk choose is odd
Now,
Total number of cards = 7
Total number of odd cards = 3
So, Probability = ³C₂ / ⁷C₂
= [tex]\frac{3!}{2! (3-2)!}. \frac{2! (7 - 2)!}{7!}[/tex]
= [tex]\frac{3!}{2! (1)!}. \frac{2! (5)!}{7!}[/tex]
= [tex]\frac{3!}{(1)!}. \frac{ (5)!}{7.6.5.4.3!}[/tex]
= [tex]\frac{ 5.4.3.2.1}{7.6.5.4}[/tex]
= [tex]\frac{1}{7}[/tex]
∴ we get
Probability that the product is an odd number = [tex]\frac{1}{7}[/tex]
