Question

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $9 for heads and $21 for tails. Your mother says she wants you to roll a six-sided die. She will give you $5 times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.

Answer 1

$30 for the flip a coin game.
$105 for the dice game.
- > heads = $9
-> tails = $21
^ $9+$21=$30

dice game-
6 sides of a dice, she doubles it by 5.
1*5 + 2*5 + 3*5 + 4*5 + 5*5 + 6*5
^ 5+10+15+20+25+30= 105.
-> $105 for dice game.

you can easily get $9/$21 from your sister, but it won’t be as much from the dice, but you have more risk going with the dice since there’s 6 sides. the highest to get from your mother is $30 and the highest from your sister is $21, but the dice is the better deal.

Answer 2

The maximum amount you can get from your mother is $30, while the most amount you can get from your sister is $21, but the dice is the better bargain.

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

 

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

The expected value of X is:

$E(X) = np$

You need to borrow money for gas, so you ask your mother and your sister.

You can only borrow money from one of them.

Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin.

She will give you $9 for heads and $21 for tails.

Your mother says she wants you to roll a six-sided die.

She will give you $5 times the number that appears on the die.

The expected value for a coin will be

$E(X) = 1 \times 0.5 = 0.5$

The expected value for a dice will be

$E(X) = 1 \times \dfrac{1}{6} = 0.1667$

You can easily receive $9/$21 from your sister, but it won't be as much as the dice, and you'll take a bigger risk with the dice because it has six sides.

The maximum amount you can get from your mother is $30, while the most amount you can get from your sister is $21, but the dice is the better bargain.

Learn more about binomial distribution here:

https://brainly.com/question/13609688

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