Countable Sample Spaces 1. Two players draw cards with replacement from a full d
ID: 3273739 • Letter: C
Question
Countable Sample Spaces
1. 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?
2. Two fair dice are rolled until sum 12 occurs. What is the probability that at least ten rolls wil be required?
3. 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?
4. 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
probability that the first player to draw wins =first card is ace+first 2 cards drawn are not ace and third card is +first 4 cards drawn are not ace and fifth card is +............ =(1/4)+(1-1/4)2*(1/4)+(1-1/4)3*(1/4)+..............
=(1/4)/(1-(3/4)2) =4/7
2)probability to get a sum of 12 =1/36
therefore probability that at least ten rolls wil be required =P(till 9 rolls 12 does not appear) =(1-1/36)9 =(35/36)9 =0.7761
3)
probability that the player making the first toss wins the game =heads cones in first toss +first two toss have tails and head comes in 3rd toss+first four toss have tails and head comes in 5th toss+.........
=(1/2)+(1-1/2)2*(1/2)+(1-1/2)4*(1/2)+........ =(1/2)/(1-(1/2)2) =2/3
4)
probability that the first heart is drawn after the fourth card =P(till 4th card no heart) =(1-13/52)4 =(39/52)4 =0.3164
please revert for any clarification required