Coin box Question: Assume that there are 25 pennies, 10 nickels, 10 dimes, and 5 quarters in a box. after shuffeling the box, you pick a coin at random and note down its face value. let x represent the face value of the coin in cents. then construct the probability distribution of x. The question I need to find is...Find P(x is at most 12) ? I am not sure what to do or how to do it. i would appreciate the help. Thanks,
To find the probability distribution of x, we first need to calculate the total number of coins in the box. In this case, we have a total of 25 + 10 + 10 + 5 = 50 coins.
Next, we list out all the possible face values of the coins:
- Pennies have a face value of 1 cent, so there are 25 pennies.
- Nickels have a face value of 5 cents, so there are 10 nickels.
- Dimes have a face value of 10 cents, so there are 10 dimes.
- Quarters have a face value of 25 cents, so there are 5 quarters.
Now, we need to calculate the probability of selecting a coin with a face value at most 12 cents (x ≤ 12). We'll consider each type of coin separately:
1. Pennies: All pennies have a face value of 1 cent. Since there are 25 pennies, the probability of selecting a penny is given by P(penny) = 25/50 = 1/2. For the given condition of x ≤ 12, the probability of selecting a penny is 1/2 since all pennies have a face value ≤ 12 cents.
2. Nickels: Out of the 10 nickels, only those with a face value less than or equal to 12 cents will satisfy x ≤ 12. The nickels with face values less than or equal to 12 cents are 5 cents, so the probability of selecting a nickel with a face value at most 12 cents is P(nickel ≤ 12) = 5/50 = 1/10.
3. Dimes: Similar to nickels, only dimes with a face value less than or equal to 12 cents will satisfy x ≤ 12. However, there are no such dimes in this case. Therefore, the probability of selecting a dime with a face value at most 12 cents is P(dime ≤ 12) = 0.
4. Quarters: The only quarter with a face value less than or equal to 12 cents is the one with a face value of 25 cents. Since there are 5 quarters, the probability of selecting a quarter with a face value at most 12 cents is equal to P(quarter ≤ 12) = 5/50 = 1/10.
Finally, to find the overall probability of selecting a coin with a face value at most 12 cents, we sum up the individual probabilities for each type of coin:
P(x ≤ 12) = P(penny) + P(nickel ≤ 12) + P(dime ≤ 12) + P(quarter ≤ 12)
= 1/2 + 1/10 + 0 + 1/10
= 4/10
= 2/5
Therefore, the probability of x being at most 12 cents is 2/5.