Respuesta :
The probability that Annie has selected the cards numbered 1, 2, and 3 is [tex](\frac{1}{720} )[/tex]
Step-by-step explanation:
Here, the total number of cards in the set = 10
The cards are numbered as 1,2,3,4,5,...., 10
P(Any event E) = [tex]\frac{\textrm{Total favorable events}}{\textrm{Total number of events}}[/tex]
P(picking a card with number 1) = [tex]\frac{\textrm{Total cards with number 1 on it}}{\textrm{Total cards}} = (\frac{1}{10})[/tex]
Now when the first card is picked, the number of cards left = 10 - 1 = 9
P(picking a card with number 2) = [tex]\frac{\textrm{Total cards with number 2 on it}}{\textrm{Total cards}} = (\frac{1}{9})[/tex]
Similarly, P(picking a card with number 3) = [tex]\frac{\textrm{Total cards with number 3 on it}}{\textrm{Total cards}} = (\frac{1}{8})[/tex]
So, the total probability that she has selected card with number 1, 2 and 3
= [tex](\frac{1}{10} ) \times (\frac{1}{9} ) \times (\frac{1}{8} ) = (\frac{1}{720} )[/tex]
Hence, the probability that she has selected the cards numbered 1, 2, and 3 is [tex](\frac{1}{720} )[/tex]
Answer:
Probability that she has selected the cards numbered 1, 2, and 3 is [tex]\frac{1}{720}[/tex] .
Step-by-step explanation:
We are given that Annie writes the numbers 1 through 10 on note cards. She flips the cards over so she cannot see the number and selects three cards from the stack.
Here, the total number of cards = 10 and the cards are numbered as 1, 2, 3 ,4, ...., 10.
Probability of any event = Favorable outcomes ÷ Total no. of outcomes
Probability of picking a card with number 1 = (1/10)
Now after the first card is picked, the number of cards left = 10 - 1 = 9
So, Probability of picking a card with number 2 = (1/9)
Similarly, Probability of picking a card with number 3 = (1/8)
The total probability that she has selected card with number 1, 2 and 3 is given by;
(1/10) * (1/9) * (1/8) = (1/720)
Therefore, the probability that she has selected the cards numbered 1, 2, and 3 is (1/720) .
