Thread: I had a few question that i can't figure out the answer Help?

If you pull one card out of a standard deck of cards, what is the probability that you pull either a Queen or a Jack?

You play a game with your friend in which you roll a die and flip a coin. If you roll an even number on the die and flip a Head on the coin you win $10, if you don’t you lose $3.
a) What is the Expected Value for this game?

b) Is this game fair?

c) If you played this game 100 times with your friend, how much would you expect to win or lose?

You are planning on having 4 children with your new spouse. What is the probability that you have exactly three boys and one girl (in any order)?

What is the probability that you do not get three tails when you flip a coin three times?

There are 52 cards in a standard deck; 4 are Queens and 4 are Jacks, and Queens and Jacks are mutually exclusive, so you have a total of 8 cards that will satisfy the requirement. Therefore, the probability of drawing either a Queen or a Jack is 8/52, or 2/13.

For the game:
You have a 50% chance of rolling an even number on the die, and a 50% chance of getting a Head on the coin flip. The probability of both occurring is 50% * 50% = 25%. Therefore, there is a 75% chance you will lose the game. The expected value of this game is $10 * 25% + (-$3) * 75% = $0.25.

I'm not exactly sure what the definition of a fair game is, so I can't answer that question.

If you play the game 100 times, the expected value is $0.25*100 = $25. You would expect to win $25.

For the four children question:
There are 2^4 = 16 ways of having four children (since each could be either a boy or a girl), and there are 4 ways of having three boys and one girl (depending on which child is the girl). Assuming equal probability of having either a boy or a girl, you have a 4/16 = 1/4 chance of this event.

For the last question:

the chance of getting 3 tails is (0.5)^3, which is 0.125.
Since it's the chance of not getting 3 tails, it's 1-0.235= 0.875

Thus 0.875 chance you do not get three tails when you flip a coin three times.