214k views
2 votes
If a fair coin is tossed four times, what is the probability of it landing

heads up at least three times? Express your answer as a common fraction.

User Garethr
by
8.6k points

2 Answers

7 votes

Answer:

1/4

Explanation:

A fair coin has a 50/50 chance of landing on heads with one flip. If it is tossed twice, this is reduced to 33/66. If tossed three times, it is reduced to 25/75.

User Jrook
by
8.1k points
4 votes

To determine the probability of getting heads up at least three times in four coin tosses, we can calculate the probability of getting exactly three heads and the probability of getting four heads, then sum these probabilities.

Probability of getting exactly three heads:

There are four tosses, and we want three of them to be heads.

The probability of getting heads in one toss is 1/2.

The probability of getting tails in one toss is also 1/2.

The number of ways to arrange three heads and one tail is given by the binomial coefficient C(4,3), which is 4.

Therefore, the probability of getting exactly three heads is C(4,3) * (1/2)^3 * (1/2)^1 = 4 * 1/8 * 1/2 = 1/4.

Probability of getting four heads:

The probability of getting heads in one toss is 1/2.

The probability of getting four heads is (1/2)^4 = 1/16.

Now, add the probabilities:

Therefore, the probability of getting heads up at least three times in four coin tosses is 5/16

User Insula
by
7.9k points