Question

You are out with friends. Half of you want to go bowling and the other half want to go to a movie. How will you make a fair decision about whether to go to a movie or go bowling using a fair coin and assuming that all of you want to go to either of the places together? (Let H = heads and T = tails)
1) Flip the coin twice. If the outcome is in the sequence HH, go to the movie. If it is not HH, go bowling.

2) Flip the coin twice. If the outcome is in the sequence HT, go to the movie. If it is TH, go bowling or repeat the process.

3) Flip the coin three times. If the outcome is in the sequence HHT, go to the movie. If it is TTT or HHH, go bowling; otherwise, repeat the process.

4) Flip the coin three times. If the outcome is in the sequence HHH or TTT, go to the movie; otherwise, go bowling.

Answer 1

Answer:

Option B

Step-by-step explanation:

Given that  Half of you want to go bowling and the other half want to go to a movie

So we must get probability for bowling = prob for movie

Option 1:  Here P(HH) = 1/4 and P(no HH) = 3/4

SInce the two are not equal this is not fair

2) Here P(HT ) =1/4 and P(TH)=1/4 and other outcomes repeat the process

This is fine and hence this option is right

3) P(HHT) = 1/8 and P(TTT or HHH) =1/8+1/8=1/4

This is biased and hence not fair

4) P(HHH or TTT) = 1/4 and P(Other options)=3/4

Biased and hence not fair

Only option B is right.