State true or false.

If I toss a coin $3$ times and get head each time, I can expect a tail to have a higher chance in the 4th toss.

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True

False

answer is B.

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Detailed Solution

Given that, toss a coin 3 times and get heads each time.
Let A be the event, then the probability of the event A is given by,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

If A be the event of getting a tail, then
n(A) = 1
n(S) = 2
The probability of getting a tail is given by,

P (A) = \frac{1}{2}

Similarly, the probability of getting a head is,

= \frac{1}{2}

If a coin is tossed, the probability of getting head or tail is

12

.
In each toss the probability of getting head is

12

.
Reasonably, it is assumed that each outcome, head

(H)

or tail

(T)

, are equally likely.
So, it should not be expected that a tail has a higher chance in the 4th toss.
Therefore, the statement is not true.
Then the correct statement is that “If I toss a coin

3

times and get heads each time, I cannot expect a tail to have a higher chance in the 4th toss.”
Hence, the statement is false.
Therefore, option 2 is correct.

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