Question

A coin is tossed twice. Let

be the event "the first toss shows heads" and
the event "the second toss shows heads".
(a) Are the events
and
independent?
Input Yes or No:
(b) Find the probability of showing heads on both tosses. Write your answer as a reduced fraction.
Answer:

Answer 1

a) No, the events A and B are not independent.

b) The probability of getting heads on both tosses is 1/4.

Step-by-step explanation:

a) A coin is tossed twice. Let be the event "the first toss shows heads" and the event "the second toss shows heads".

In this case, the events A and B are not independent.

b) To determine whether the events A and B are independent, we can compare the probabilities of each event individually with the probability of both events occurring together.

P(A) = probability of getting a heads on the first toss = 1/2

P(B) = probability of getting a heads on the second toss = 1/2

P(A and B) = probability of getting heads on both tosses:

= 1/2 * 1/2

= 1/4

Since P(A and B) is not equal to P(A) * P(B), the events A and B are not independent.

The probability of getting heads on both tosses is 1/4.