What is the sample space when tossing two coins, and how can we find the probability of getting exactly one head?

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Tossing two coins involves looking at all the possible outcomes that can result from the toss. The sample space for this event consists of all combinations of heads (H) and tails (T) that can occur when the two coins are tossed.

When you toss two coins, the possible outcomes are:

  • HH (both coins show heads)
  • HT (the first coin shows heads, the second coin shows tails)
  • TH (the first coin shows tails, the second coin shows heads)
  • TT (both coins show tails)

Thus, the sample space, denoted as S, can be expressed as:

S = {HH, HT, TH, TT}

Now, to find the probability of getting exactly one head, we need to identify how many outcomes in the sample space give us exactly one head:

  • HT (first coin heads, second coin tails)
  • TH (first coin tails, second coin heads)

There are a total of 2 favorable outcomes (HT and TH) that result in exactly one head.

The probability (P) of an event is calculated using the formula:

P(Event) = Number of Favorable Outcomes / Total Number of Outcomes

Here, we have:

  • Number of Favorable Outcomes = 2 (HT and TH)
  • Total Number of Outcomes = 4 (HH, HT, TH, TT)

Therefore, the probability of getting exactly one head when tossing two coins can be calculated as:

P(exactly 1 head) = 2 / 4 = 1 / 2

In conclusion, the probability of tossing exactly one head when flipping two coins is 1/2.

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