Respuesta :
Answer:
The Probability found is:
P = [tex]\frac{13}{18}[/tex]
Step-by-step explanation:
Let x be the 10 cents coin.
Let y be the 25 cents coin.
We have to find all the possible outcomes
1) First coin = 10 cents, Second coin = 10 cents , so
(x,x) = 20
2) First coin = 10 cents, Second coin = 25 cents , so
(x,y) = 35
3) First coin = 25 cents, Second coin = 10 cents , so
(y,x) = 35
4) First coin = 25 cents, Second coin = 25 cents , so
(y,y) = 50
Find the probability of each outcome:
P(x,x) = [tex]\frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}[/tex]
P(x,y) = [tex]\frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}[/tex]
P(y,x) = [tex]\frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}[/tex]
P(y,y) = [tex]\frac{4}{9}\cdot\frac{3}{8}=\frac{12}{72}[/tex]
Add all the probabilities where sum is at least 35 i.e P(x,y) , P(y,x) , P(y,y)
P(x,y) + P(y,x) + P(y,y) = [tex]\frac{20}{72}+\frac{20}{72}+\frac{12}{72} = \frac{52}{72}=\frac{13}{18}\\[/tex]
The probability that the two coins together will be worth at least 35 cents is 13/18 and this can be determined by using the concept of probability.
Given :
- Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each.
- She chooses two of these coins at random.
The following steps can be used in order to determine the probability that the two coins together will be worth at least 35 cents:
Step 1 - The probability that the first coin is of 10 cents and the second coin is of 10 cents is calculated as:
[tex]P_1 = \dfrac{5}{9}\times \dfrac{4}{8}=\dfrac{20}{72}[/tex]
Step 2 - The probability that the first coin is of 10 cents and the second coin is of 25 cents is calculated as:
[tex]P_2 = \dfrac{5}{9}\times \dfrac{4}{8}=\dfrac{20}{72}[/tex]
Step 3 - The probability that the first coin is of 25 cents and the second coin is of 10 cents is calculated as:
[tex]P_3 = \dfrac{5}{9}\times \dfrac{4}{8}=\dfrac{20}{72}[/tex]
Step 4 - The probability that the first coin is of 25 cents and the second coin is of 25 cents is calculated as:
[tex]P_4 = \dfrac{4}{9}\times \dfrac{3}{8}=\dfrac{12}{72}[/tex]
Step 5 - So, the probability that the two coins together will be worth at least 35 cents is:
[tex]P = P_1+P_2+P_3+P_4\\\\ P = \dfrac{20}{72}+\dfrac{20}{72}+\dfrac{20}{72}+\dfrac{12}{72}\\\\P = \dfrac{13}{18}[/tex]
The probability that the two coins together will be worth at least 35 cents is 13/18.
For more information, refer to the link given below:
https://brainly.com/question/795909
