Respuesta :
Given:
Seventy cards are numbered 1 through 70, one number per card. One card is randomly selected from the deck.
To find:
The probability that the number drawn is a multiple of 3 and a multiple of 5.
Solution:
Total number from 1 to 70 = 70
Multiple of 3 from 1 to 70 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69.
Multiple of 5 from 1 to 70 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70.
Numbers which are multiply of both number 3 and 5 = 15, 30, 45, 60
Number of favorable outcomes = 4
[tex]Probability=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]Probability=\dfrac{4}{70}[/tex]
[tex]Probability=\dfrac{2}{35}[/tex]
Therefore, the required probability is [tex]\dfrac{2}{35}[/tex].
