A sorcerer has hidden an M&M in one of an infinite row of boxes. You need to find it as quickly as possible. As a matter of fact, you only have time to look in 11 boxes. The sorcerer says that he will give you a hint, by tossing a coin 100 times, and counting the number of heads, all in a flash. He will then tell you the sum of the number that the box is in, and the number of heads that he got out of 100 tosses. If the sum is 75, you decide to look in boxes 20 through 30. What is the chance that you will locate the M&M? Choose the closest answer.

Given that a sorcerer has hidden an M&M in one of an infinite row of boxes. You need to find it as quickly as possible. As a matter of fact, you only have time to look in 11 boxes. The sorcerer says that he will give you a hint, by tossing a coin 100 times, and counting the number of heads, all in a flash. He will then tell you the sum of the number that the box is in, and the number of heads that he got out of 100 tosses. If the sum is 75, you decide to look in boxes 20 through 30.

You select 20 to 30 because you think that coin resulted in 50 heads. If that was accurate then you would have full chance to locate M&M

Hence prob that you will locate the M&M

= Prob (no of heads = 50 in 100 tosses)

= [tex]100C50 (0.50)^{50} (1-0.50)^{50}\\=0.07958[/tex]

=0.08