Question

michael performed an experiment where he tossed two coins, one dime and one nickel, at the same time and recorded whether each one landed on heads or tails. his results are shown in the table below.

		nickel
dime	heads	27	26
	tails	24	23

for what percent of the tosses did the dime michael tossed land on heads?

Explanation:

Step1: Find total tosses with dime heads

To find the number of tosses where the dime landed on heads, we add the number of times the nickel was heads and tails when the dime was heads. So, \(27 + 26 = 53\)? Wait, no, wait. Wait, actually, the total number of tosses where dime is heads is the sum of (dime heads, nickel heads) and (dime heads, nickel tails). But also, we need the total number of tosses. Wait, first, let's find the number of times dime landed on heads: when dime is heads, nickel can be heads (27) or tails (26). So total for dime heads: \(27 + 26 = 53\)? Wait, no, wait, maybe I miscalculated. Wait, no, let's check the table again. The table is:

Dime \ Nickel | Heads | Tails
--- | --- | ---
Heads | 27 | 26
Tails | 24 | 23

So total number of tosses: \(27 + 26 + 24 + 23 = 100\) (since 27+26=53, 24+23=47, 53+47=100).

Number of tosses where dime landed on heads: \(27 + 26 = 53\).

Wait, but the question is "For what percent of the tosses did the dime Michael tossed land on heads?" So we need to find (number of dime heads tosses / total tosses) * 100.

Total tosses: \(27 + 26 + 24 + 23 = 100\).

Number of dime heads: \(27 + 26 = 53\). Wait, no, wait: 27 (dime H, nickel H) + 26 (dime H, nickel T) = 53. Then total tosses: 53 (dime H) + 24 (dime T, nickel H) + 23 (dime T, nickel T) = 53 + 24 + 23 = 100. So the percentage is (53 / 100) * 100 = 53%? Wait, no, wait, that can't be. Wait, maybe I made a mistake. Wait, 27 + 26 is 53, 24 + 23 is 47, 53 + 47 is 100. So 53 out of 100 is 53%. But let me check again.

Wait, the table:

• Dime Heads, Nickel Heads: 27
• Dime Heads, Nickel Tails: 26
• Dime Tails, Nickel Heads: 24
• Dime Tails, Nickel Tails: 23

So total tosses: 27 + 26 + 24 + 23 = 100.

Number of tosses with Dime Heads: 27 + 26 = 53.

So percentage is (53 / 100) * 100 = 53%. Wait, but that seems correct? Wait, maybe I miscalculated the sum. 27 + 26 is 53, 24 + 23 is 47, 53 + 47 is 100. So yes, 53 out of 100 is 53%.

Wait, but let me confirm. The formula for percentage is (number of favorable outcomes / total number of outcomes) 100. Here, favorable outcomes are dime heads, which is 27 + 26 = 53. Total outcomes is 100. So (53 / 100) 100 = 53%. So the percentage is 53%.

Wait, but maybe I made a mistake in adding. Let's add again:

27 (dime H, nickel H) + 26 (dime H, nickel T) = 53.

24 (dime T, nickel H) + 23 (dime T, nickel T) = 47.

53 + 47 = 100. Correct.

So 53 / 100 = 0.53, times 100 is 53%. So the answer is 53%.

Wait, but let me check again. Maybe the total number of tosses is not 100? Wait, 27 + 26 is 53, 24 + 23 is 47, 53 + 47 is 100. So yes, total tosses is 100. So 53% is the answer.

Step1: Calculate total tosses with dime heads

Sum the number of tosses where dime is heads (nickel heads and nickel tails): \(27 + 26 = 53\).

Step2: Calculate total number of tosses

Sum all tosses: \(27 + 26 + 24 + 23 = 100\).

Step3: Calculate the percentage

Divide the number of dime heads tosses by total tosses and multiply by 100: \(\frac{53}{100} \times 100 = 53\%\).

Answer:

53%