Find the expected value of the winnings from a game that has the following
payout probability distribution:
Payout ($)| 0 4 6 8 10
Probability 0.45 0.3 0.1 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.

2.65

Step-by-step explanation:

Multiply each payout by its probability, then add those products.

See the attached image.

The first column has the payouts.  The second column has the probabilities. The third column has the results of multiplying a payout by its probability.

The sum of the entries in the third column is 2.65

coins of silver or gold

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.