Question

Determine whether the successive probabilities are independent or dependent events.

15) The probability of getting 4 tails in a row when flipping a coin?
a) Independent
b) Dependent

16) The probability of drawing 2 Queens in a row from a deck of cards?
a) Independent
b) Dependent ​

Answer 1

15) a) independent

16) b) Dependent ​

Explanation:

15) let T1 be the event : “get a tail in the first flip”

let T2 be the event : “get a tail in the second flip”

p(T1 ∩ T2) = 1/4

p(T1) = 1/2

p(T2) = 1/2

Then

p(T1) × p(T2) = (1/2)(1/2 = 1/4

Since ,p(T1 ∩ T2) = 1/4 = p(T1) × p(T2)

Then the events are independent.

16) These events are dependent since we don’t replace the Queen before the second draw.

The two Events are dependent because the probability that we draw a Queen in the first draw affect the probability that we draw a Queen in the second draw.