An unbiased coin is tossed untill the first head appears or until four tosses are completed, whichever earlier. Which of the following statement is/are correct?
1. The probability that no head is observed is `(1)/(16)`.
2. The probability that the experiment ends with three tosses is `(1)/(8)`.
Select the correct anser using the code given below.

Options

A. 1 only
B. 2only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

C

Explanation

`S={H,TH,"TTH","TTTH","TTTT"}`
`P(T)=P(H)=(1)/(2)`
[Probability of gettiing head or tail in a single toss]
`therefore` Probability that no head is observed=`P("TTTT")`
=P(T)P(T)P(T)P(T)
`=(1)/(2^(4))=(1)/(16)`
And the probability that hte experiment ends with 3 tosses
`=P("TTH")`
`=P(T)P(T)P(H)`
`=(1)/(8)`
Hence both statements are correct