Question

On a particular day, Vidhi and Unnati couldn’t decide on who would get to drive the car. They had one coin each and flipped their coin exactly three times.

The following was agreed upon: 

1. If Vidhi gets two heads in a row, she would drive the car.
2. If Unnati gets a head immediately followed by a tail, she would drive the car. 

Who has greater probability to drive the car that day? Justify your answer.

Answer 1

When a coin is flipped 3 times, the total number of possible outcomes is 2³ = 8.

(S) = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Case 1: Vidhi drives the car:

Vidhi drives the car if she gets two heads in a row, i.e., the pattern HH appears.

Favourable outcomes for Vidhi:

HHH 

HHT

THH

There are 3 favorable outcomes.

The total number of outcomes is 8.

P(Vidhi) = `3/8`

Case 2: Unnati drives the car:

Unnati drives the car if she gets H immediately followed by T, i.e., the pattern HT appears.

Favourable outcomes for Unnati:

HHT 

HTH 

HTT

THT 

There are 4 favorable outcomes.

The total number of outcomes is 8.

P(Unnati) = `4/8`

Compare the two probabilities:

P(Vidhi) = `3/8` = 0.375

P(Unnati) = `4/8` = 0.5

Since `4/8 > 3/8`

Unnati has a greater probability to drive the car.