A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?

1/4 Chances.

0.25% Chances

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

The first toss gives two possible outcomes: T or H ( in blue)

The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

           S={(H,H),(H,T),(T,H),(T,T)}

with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

           E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

           P(E)=n(E)n(S)=14

Method 2: Use the product rule of two independent event

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

           P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

          P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

0.25

Step-by-step explanation:

Probability is how likely something is to happen

The probability of an event happening = (number of ways it can happen) ÷ (total number of outcomes)

With a coin toss there are 2 outcomes: head or tail

The number of ways tossing a tail can happen is 1.

⇒ probability of getting a tail = 1/2 = 0.5

As any tosses are independent of any previous tosses, the probability of the second toss will not be affected by the first toss.  

Therefore, the probability of getting a tail in the first toss = 0.5

and the probability of getting a tail in the second toss = 0.5

We can calculate the chances of two or more independent events by multiplying the chances.

Therefore, the probability of getting a tail in the first toss AND in the second toss = 0.5 x 0.5 = 0.25 (since they are independent events)

good luck on your studies! : )

david edward.