Question

A die is cast twice and a coin is tossed twice. what is the probability that the die will turn a 6 each time and the coin will turn a tail every time?

Answer 1

Answer:

Total possible outcomes (for the die and coin) = 36 + 4 = 40.

Total favourable outcomes = 1 + 1 = 2

P(E)= 2/40 = 1/20.

Answer 2

Answer:

The two events i.e. casting the die and tossing the coin are independent, and the probability of both the events $\frac{1}{144}$

Step-by-step explanation:

The Rule of products is only applicable to events that are independent of each other. The product gives the total probability of such events. In other words, the probability of all such events occurring is what we get from the product of probabilities.

Each time the die is cast, it is an independent event. The probability of a getting a 6 is =$\frac{1}{6}$. So the probability of getting a 6 when the die is cast twice $=\frac{1}{6} * \frac{1}{6} = \frac{1}{36}$

Similarly the probability of getting a tail in two flips that follow each other (are independent) $=\frac{1}{2} *\frac{1}{2} =\frac{1}{4}$

Therefore as the two events i.e. casting the die and tossing the coin are independent, the probability of both the events $=\frac{1}{36}*\frac{1}{4}=\frac{1}{144}$