Binomial distribution for a biased coin - Please help

[Aiswarya_M]

Question: "You are given a biased coin with a probability of seeing a head is p = 0.6 and the probability of seeing a tail is q = 0.4. Suppose you toss the coin 10 times. What is the probability of you getting a head for the first time on your fourth attempt?"

It will be very helpful if someone could give me the answer to the question along with the explanation. Thanks.

 

[Dr.Peterson]

Clearly you have learned something about the binomial distribution. Do you see that p = 0.6, and n = 10?

But this question does not really involve the binomial distribution! The probability that your first head is on the fourth toss means P(TTTH). What is the probability that you toss tails, then tails, then tails, then heads? (What comes after is irrelevant.)

 

[Steven G]

It will be very helpful if someone could give me the answer to the question along with the explanation. Thanks.

Welcome to the forum.
In this forum we do no give out answers, rather we help the student arrive at the answer on their own by giving leading hints (As Dr Peterson did in his post).
So what we need from you is for you to tell us where you are stuck or even better if you show us the work you already tried.

 

[Aiswarya_M]

To get the sequence TTTH with p=0.6, x=4; I tried: (¹⁰C₀(1-p)⁰p¹⁰)+(¹⁰C₁(1-p)¹p⁹)+(¹⁰C₂(1-p)²p⁸)+(¹⁰C₃(1-p)³p⁷)+(¹⁰C₄(1-p)⁶p⁴) or is it 0.4*0.4*0.4*0.6?

 

[Dr.Peterson]

Can you tell us the reasoning behind each of those? One of them is correct; the goal is for you to see why. Also, what is the actual meaning of the other?