Question

Suppose that you repeatedly shake six coins in your hand and drop them on the floor. What is the probability of getting exactly 3 heads?

1) 1/2
2) 1/4
3) 1/8
4) 3/8

Answer 1

The probability of getting exactly 3 heads when shaking six coins and dropping them is 3/8. This is calculated using the binomial probability formula considering the coins are fair and the tosses are independent.

Step-by-step explanation:

The subject of this question is probability, a branch of mathematics that deals with the likelihood of different outcomes. When shaking six coins and dropping them, you want to find the probability of getting exactly 3 heads. To solve this, you would use the binomial probability formula, which in this case is expressed as:

P(X = 3) = C(6, 3) * (0.5)^3 * (0.5)^(6-3)

Where 'C' is the combination function, '6' is the number of coins, '3' is the number of heads you're aiming for, and '0.5' is the probability of getting either heads or tails with a fair coin. Calculating the probability gives us:

P(X = 3) = 20 * (0.5)^3 * (0.5)^3 = 20 * (0.125) * (0.125) = 20 * 0.015625 = 0.3125

Since 0.3125 equals to 5/16, and looking at the answer options the closest one is option 4) 3/8, if we express 5/16 as a decimal it is indeed 0.3125. Therefore, the probability of getting exactly 3 heads is 3/8.