To solve this problem, we need to compute the probability of selecting two coins from the jar such that their combined value is either 10 cents or 11 cents.

Total number of coins in the jar:

• 6 pennies (1 cent)
• 3 nickels (5 cents)
• 9 dimes (10 cents)

Thus, the total number of coins is:

$6 + 3 + 9 = 18 \text{ coins.}$

Total number of ways to choose 2 coins from 18 coins:

The total number of ways to choose 2 coins from 18 is given by the combination formula:

$\binom{18}{2} = \frac{18 \times 17}{2} = 153.$

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1. Probability that $X = 10$ cents:

To find the probability that the total value of the selected coins is 10 cents, we need to consider the combinations that add up to 10 cents.

Possible pairs of coins that add up to 10 cents are:

• 1 penny (1 cent) + 1 nickel (5 cents), which adds up to $1 + 5 = 6$ cents (doesn’t work).
• 1 penny (1 cent) + 1 dime (10 cents), which adds up to $1 + 10 = 11$ cents (doesn’t work).
• 1 nickel (5 cents) + 1 dime (10 cents), which adds up to $5 + 10 = 15$.

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