Question

An experiment consists of tossing an unfair coin (48% 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?
b. Does the probability change if we toss the coin three times? What if we toss the coin four times?

Answer 1

a.
`Probability = 0.2496`

b. No, it won't change

Explanation:

Represent
`the\ head` with H and
`Tail\ with` T

Such that:

`P(H) = 48\%`

Solving (a): First head in second trial

First, we determine P(T) i.e. the probability of obtaining a tail

`P(H)+P(T) = 100\%`

`P(T) = 100\% -P(H)`

Substitute 48% for P(H)

`P(T) = 100\% -48\%`

`P(T) = 52\%`

If the first head is obtained in the second trial, the probability is:

`Probability = P(T\ and\ H)`

`Probability = P(T)\ and\ P(H)`

`Probability = P(T)\ *\ P(H)`

`Probability = 48\%* 52\%`

`Probability = 0.2496`

Solving (b): Will it change if tossed three or four times?

Irrespective of the number of times the coin is tossed, the probability of obtaining a head in the second toss will always be the same because the coin has to be tossed twice before the third and the fourth time.