A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play. Should you play the game?

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

Step-by-step explanation:

Given - A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play.

To find - Should you play the game?

Formula used -

Expected value , E[x] = ∑x p(x)

where p(x) is the probability.

Proof -

Given that,

Total blue marbles in a bag = 10

Total yellow marbles in a bag = 3

Total orange marbles in a bag = 12

So,

Total number of marbles in a bag = 10 + 3 + 12 = 25

Now,

Probability of getting blue marble =

Probability of getting yellow marble =

Probability of getting orange marble =

So,

Expected value , E[x] = ∑x p(x)

                                   = (10)( ) + (15)() + (-10)()

                                   =

                                   =

                                   =

                                   = 1

So,

Expected value = 1

So,

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: