Question 71

# Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops.At which mark does he stop?A. He stops after 21 coin tosses.B. He obtains three more tails than heads.

Solution

Consider Statement A:

B_ _x_R

If the person has to reach red, then he has to take 2 steps in the most simplest manner. Now suppose he first takes left step and then tkes a right step. Â He has taken 2 steps and has to take further 2 steps in order to reach red. In this way, a person has to take even number of steps to reach red. In the similar manner, a person has to take three steps to reach blue in the simplest manner. It means he would have to take odd number of steps to reach blue and since 21 is an odd number, therefore the person would reach blue step.

Consider Statement B,

It is given that the person obtains 3 more tails as compared to heads. Take the case of 1 head and four tails. In this case, he would reach blue step.Now take the case of 2 heads and 5 tails. In this case 2 heads are neutralised by 2 tails. The ramaining portion is 3 tails which would help to reach blue steps. In this manner, no matter how many heads are, three more tails would make sure that the person reaches blue corner.Â Â

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