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Question

What is the probability that a head is obtained, followed by a tail, if a coin is flipped twice?

A
1
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B
12
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C
14
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D
34
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Solution

The correct option is C 14

Let P(H) be the probability of obtaining head when a coin is flipped.
Total possible outcomes ={H,T}
Favorable outcome ={H}

Number of favorable outcome =1
Total number of outcomes =2

P(H)=Number of favorable outcomeTotal number of outcomes

P(H)=12


Let P(T) be the probability of obtaining tail when a coin is flipped.
Total possible outcomes ={H,T}
Favorable outcome ={T}

Number of favorable outcome =1
Total number of outcomes =2

P(T)=Number of favorable outcomeTotal number of outcomes

P(T)=12


Let P(H and T) denotes the probability of obtaining head followed by a tail. This probability would be obtained by multiplying P(H) and P(T) as both these events are Independent events.

P(H and T)=P(H)×P(T)

P(H and T)=12×12

P(H and T)=14


The probabilty P(H and T) of obtaining a head followed by a tail is 14.

Alternate Solution:–––––––––––––––––––––

The sample space S obtained when a coin is flipped twice is:
S={HH,HT,TH,TT}

We need to find the probabilty P(H and T) of obtaining a head followed by a tail.
Favorable outcome ={HT}

Number of favorable outcome =1
Total number of possible outcomes =4

P(H and T)=14


The probabilty P(H and T) of obtaining a head followed by a tail is 14.

Therefore, option (c.) is the correct answer.

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