Countable Sample Spaces 1. A roulette wheel (containing 36 number 1,2,3...36 and
ID: 3300352 • Letter: C
Question
Countable Sample Spaces
1. A roulette wheel (containing 36 number 1,2,3...36 and two house numbers 0 and 00) is spun until the number 7 comes up. What is the probability that the number 7 will come up in hte first ten spins.
2. Two players draw cards with replacement from a full deck until one of them draws an ace. What is the probability that the first player to draw wins?
3. Two fair dice are rolled until sum 12 occurs. What is the probability that at least ten rolls wil be required?
4. Two people toss a coin until one of them gets a head. What is the probability that the player making the first toss wins the game?
5. Cards are drawn with replacement from a fulll deck of 52 cards until a heart is drawn. What is the probability that the first heart is drawn after the fourth card?
Explanation / Answer
Question 1:
There are 36 numbers, therefore the probability of getting a number 7 would be 1/36 as each of the 36 numbers are equally likely. Now the probability that the number 7 will come up in the first ten spins is computed as:
= 1 - Probability that the number 7 does not come up in the first 10 spins
= 1 - (35/36)10
= 0.2455
Therefore 0.2455 is the required probability here.