Question

An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified number of times and recording the outcomes.

(a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.)

Does this probability change if we toss the coin three times? What if we toss the coin four times?

The probability changes if we toss the coin three times, but does not change if we toss the coin four times.The probability does not change for either three or four tosses.    The probability changes for both three and four tosses.The probability changes if we toss the coin four times, but does not change if we toss the coin three times.

What probability distribution model do we use to compute these probabilities?

geometricpoisson    normalbinomial

(b) What is the probability that the first head will occur on the fourth trial? after the fourth trial? (Use 4 decimal places.)

P(4)
P(n > 4)

Answer 1

Answer:

a)

Given,

To determine the probability that the first head will occur on the second trial

Probability = P(Tail & Head)

= (1 - 0.53)*0.53

= 0.2491

b)

The required probability = P(Tail,Tail & Head)

= (1 - 0.53)*(1 - 0.53)*0.53

= 0.1171

Here by observing the given data we can say that,

The probability changes for both three and four tosses.

c)

Here the given trails are independent & the 1st success occur in the nth trail.

So that, we can use

Geometric distribution model.

i.e.,

Option A is right answer.

d)

To determine the probability that the first head will occur on the fourth trial? after the fourth trial

consider,

P(4) = P(TTTH)

= (1-0.53)*(1-0.53)*(1-0.53)*0.53

= 0.0550

Now,

P(n > 4) = P(All first 4 are tails)

= (1 - 0.53)^4

= 0.47^4

= 0.0488