Answer:
1) Probability X = 10 is 20.59%.
2) Probability X = 11 is 6.62%.
3) Expected value of X = 12.12
Step-by-step explanation:
We are given;
Amount of pennies in jar = 3
Amount of nickels in jar = 8
Amount of dimes in jar = 6
Total number of coins in the jar = 3 + 8 + 6 = 17 coins
Now, it is well known that;
1 penny = 1 cent
1 nickel = 5 cents
1 dime = 10 cents
A) Probability X = 10 cents
To achieve 10 cents by selecting two coins from the jar means both coins must be nickels.
Thus;
For the first selection, the probability of selecting a nickel would be 8/17.
The probability that the second coin is also a nickel is 7/16.
the probability of this outcome is; 8/17 × 7/16 = 7/34 = 20.59%.
2)Probability X = 11 cents
To achieve 11 cents by selecting two coins from the jar means one coin must be a penny while the other must be a dime.
For the first selection, the probability of selecting a penny is 3/17. The probability of selecting a dime in the second selection is 6/16.
the probability of this outcome is; 3/17 × 6/16 = 9/136 = 6.62%.
3) The expected value of X will be;
E(X) = 2[(3 × 1) + (8 × 5) + (6 × 10)]/(3 + 8 + 6)
E(X) = 2(103)/17
E(X) = 206/17
E(X) = 12.12
