Problem Solving

In his ranch, Doug Bo can place a loop of rope, called a lasso, once in every 2 throws around a cow's neck. What is the probability that he will be able to place a lasso around a cow's neck at least once in 5 attemps?

(A) 1/5
(B) 15/32
(C) 1/2
(D) 31/32
(E) 1

The OA is D.

I'm confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

LUANDATO wrote:In his ranch, Doug Bo can place a loop of rope, called a lasso, once in every 2 throws around a cow's neck. What is the probability that he will be able to place a lasso around a cow's neck at least once in 5 attemps?

(A) 1/5
(B) 15/32
(C) 1/2
(D) 31/32
(E) 1

The OA is D.

I'm confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

First, P(x) = 1 - P(Not x)

So, P(at least one success in five attempts) = 1 - P(no successes in five attempts)

If Doug Bo succeeds once every two tosses, we know the probability is 1/2 that each attempt is successful. (And the probability of failure is also 1/2)

P(no successes in five attempts) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32

1 - P(no successes in five attempts) = 1 - 1/32 = 31/32. The answer is D