Question

A coin is tossed any number of times until a head appears. If x denotes the number of tosses till head appear then P(x≥3)=

Answer 1

Answer:

P(x>_3)= 1

Step-by-step explanation:

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Answer 2

Answer: Probability that head will appear at or after third toss ,i.e. P(x≥3) , is equal to 1/4 .

Step-by-step explanation:

P(x) ⇒ Probability of heads appearing for first time at xth toss.

Sum of probabilities is 1.

Therefore,

⇒ P(x=1) + P(x=2) + P(x≥3) = 1

⇒ P(x≥3) = 1 - P(x=1) - P(x=2)

P(x=1) ⇒ Head appears in first toss = $\frac{1}{2}$

P(x=2) ⇒ Head appears in second toss ⇒ Tails appears in first toss

P(x=2) = Probability of tails at toss1 × Probability of heads at toss2

P(x=2)  =   $\frac{1}{2}$ × $\frac{1}{2}$ = $\frac{1}{4}$

Substituting P(x=1) and P(x=2) in  P(x≥3) = 1 - P(x=1) - P(x=2) ,

⇒ P(x≥3) = $1 - \frac{1}{2} - \frac{1}{4}$  

P(x≥3) = 1/4

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