What is the expected value when a $1 lottery ticket is bought in which the purchaser wins exactly $10 million if the ticket contains the six winning numbers chosen from the set {1, 2, 3,…, 50} and the purchaser wins nothing otherwise?

We expect to lose $0.37 per lottery ticket

Explanation:

six winning numbers from = { 1, 2, 3, ....., 50}

So, the probability of winning:

The probability of losing would be:

P(loss) = 1 - P(win)

According to the question,

When we win, then we gain $10 million and lose the cost of the lottery ticket.

So,

$10,000,000 - 1 = $9,999,999

When we lose, then we lose the cost of the lottery ticket = $1

The expected value is the sum of the product of each possibility x with its probability P(x):

E(x) = ∑ xP(x)

Thus, we expect to lose $0.37 per lottery ticket

ans.

heterothermic organisms include those organisms that can switch between homeothermic (having body temperature higher than environment) and poikilothermic (having variation in internal body temperature) strategies.

some migratory birds show heterothermy as they decrease their metabolic rate during cold nights to keep their body temperature low. drop in metabolic rate allows increase in production efficiency of birds that reduces the internal body temperature to make it equal to external cold temperature during cold nights.

thus, the correct answer is 'birds allow their temperature drop in order to increase their production efficiency.'