Question

You toss a coin twice. Which calculation proves that landing on tails for the first toss and heads on the second toss are independent events?

Answer 1

i dont completely understand the question so if im wrong im sorry but i think the answer is a 1out 2 percent chance if it lands on tails some with heads

Answer 2

Answer with explanation:

If a coin is tossed twice than the sample space of outcomes are:

{ HH, HT, TH, TT}

Now let A denote the event that the tail comes up in the first toss

and B denote the event that head comes up on the second toss.

Let P denote the probability of an event.

Hence,

P(A)=1/2  ( As probability of tail is half during  single toss)

Similarly P(B)=1/2 ( Since , Probability of obtaining a head is half on a single toss)

Also,

P(A∩B)=1/4

( Since the outcomes is TH )

Now, as:

P(A∩B)=P(A)×P(B)

Hence,  landing on tails for the first toss and heads on the second toss are independent events.