A die is thrown and a coin is then tossed as many times as the number shown by the die. What is the probability of getting more number of heads than tails?
(47 ,87,77,97) / 192
Probability of each number on die = 1/6
E = Event when head occurs more number of times than tails
When 1 is rolled: P(E) = 1/2 (H)
When 2 is rolled: P(E) = 1/4 (HH)
When 3 is rolled: P(E) = 1/8 (HHH) + 3/8 (HHT)
When 4 is rolled: P(E) = 1/16 (HHHH) + 4/16 (HHHT)
When 5 is rolled: P(E) = 1/32 (HHHHH) + 5/32 (HHHHT) + 10/32 (HHHTT)
When 6 is rolled: P(E) = 1/64 (HHHHHH) + 6/64 (HHHHHT) + 15/64 (HHHHTT)
Whenever a die is thrown odd number of times, there are equal cases when Heads are more than Tails, and Tails are more than heads, -> P(H more) = 1/2
Whenever a die is thrown even number of times, there are three types of cases, Heads = Tails, Heads > Tails , Tails > Heads. If we remove the Heads = Tails case, and divide the remaining probability by 2, we will get P(H more) = 1/2 * ( 1 - P(H=T))
Using the above we get 1/6 *( 1/2 + 1/4 + 1/2 + 5/16+ 1/2 + 22/64) = 77/192..
Second method is shorter I think...
PS: Figured out the shorter method while doing the question.. Damn !
Two white squares and a black square have to be chosen from a chess board such that no two of them are in the same row or column. In how many ways can the selection be made?
Whenever a die is thrown odd number of times, there are equal cases when Heads are more than Tails, and Tails are more than heads, -> P(H more) = 1/2
Whenever a die is thrown even number of times, there are three types of cases, Heads = Tails, Heads > Tails , Tails > Heads. If we remove the Heads = Tails case, and divide the remaining probability by 2, we will get P(H more) = 1/2 * ( 1 - P(H=T))
Using the above we get 1/6 *( 1/2 + 1/4 + 1/2 + 5/16+ 1/2 + 22/64) = 77/192..
Second method is shorter I think...
PS: Figured out the shorter method while doing the question.. Damn !
gud one .........sir....!!yes it is shorter.........!! but waha cat mai click hona chayee....!!
second method mujhe kabhi click ni hota.........!!
Whenever a die is thrown odd number of times, there are equal cases when Heads are more than Tails, and Tails are more than heads, -> P(H more) = 1/2
Whenever a die is thrown even number of times, there are three types of cases, Heads = Tails, Heads > Tails , Tails > Heads. If we remove the Heads = Tails case, and divide the remaining probability by 2, we will get P(H more) = 1/2 * ( 1 - P(H=T))
Using the above we get 1/6 *( 1/2 + 1/4 + 1/2 + 5/16+ 1/2 + 22/64) = 77/192..
Second method is shorter I think...
PS: Figured out the shorter method while doing the question.. Damn !