find the probability of obtaining at the most 1 head in 5 tosses of a fair coin
To find the probability of obtaining at most 1 head in 5 coin tosses, we can consider the following possibilities:
1 head and 4 tails
0 heads and 5 tails
First, let's calculate the probability of getting exactly 1 head and 4 tails.
The probability of getting a head on a single coin toss is 1/2, and the probability of getting a tail is also 1/2.
Therefore, the probability of getting 1 head and 4 tails is:
(1/2)^1 * (1/2)^4 = 1/16
Next, let's calculate the probability of getting exactly 0 heads and 5 tails.
The probability of getting a tail on a single coin toss is 1/2.
Therefore, the probability of getting 0 heads and 5 tails is:
(1/2)^0 * (1/2)^5 = 1/32
To find the probability of obtaining at most 1 head in 5 tosses, we need to sum up the probabilities of the two possibilities:
P(at most 1 head) = P(1 head and 4 tails) + P(0 heads and 5 tails)
= 1/16 + 1/32
= 1/16 + 1/32
= 3/32
Therefore, the probability of obtaining at most 1 head in 5 tosses of a fair coin is 3/32.