Question

A coin is tossed five times. What is the probability of getting at least one tail?

A) 1/32
B) 31/32
C) 1/2
D) 15/16

Answer 1

The probability of getting at least one tail when tossing a coin five times is arrived at by subtracting the probability of getting all heads (1/32) from the total probability (1), which results in 31/32. Option B is the correct answer.

Step-by-step explanation:

The question is asking for the probability of getting at least one tail when a coin is tossed five times. To calculate this, instead of finding the individual probabilities of getting 1, 2, 3, 4, or 5 tails (which would be time-consuming), it is easier to calculate the probability of the opposite event - not getting any tails at all, which means getting all heads - and then subtract that value from 1 (the total probability of all possible outcomes).

Since each flip of a fair coin yields heads with a 50-50 chance, the probability of getting heads in one flip is 0.5. Thus, the probability of getting heads 5 times in a row would be 0.5 raised to the fifth power (0.5^5) which equals 1/32. Therefore, the probability of getting at least one tail would be 1 – (1/32), which gives us 31/32.

So the correct option is B) 31/32.

Answer 2

Answer: B) 31/32

Explanation

There are p = 2 sides to each coin and q = 5 coins.

That gives p^q = 2^5 = 32 different outcomes. One example is HHTHH where H is heads and T is tails.

Of those 32 outcomes, only HHHHH has all 5 heads and no tails. So the other 32-1 = 31 combos have at least one tail.

That's how we arrive at 31/32