High School

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A coin is tossed three times. The probability of getting a head is:

Working out:
3 tosses are: 2x2x2 = 8 possible outcomes
Single toss is P(H)=0.5
P(TTT)=0.5x0.5x0.5=0.125
1-P(TTT) = 1-0.125=0.875

Answer :

To determine the probability of getting at least one head when a coin is tossed three times, we can follow these steps:

When you toss a coin, each toss has two possible outcomes: heads (H) or tails (T). Therefore, when a coin is tossed three times, the total number of possible outcomes is:

[tex]2 \times 2 \times 2 = 8[/tex]

These outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

The probability of getting a head on any single toss is [tex]0.5[/tex]. Therefore, the probability of getting three tails (TTT) in a row is calculated by multiplying the probability of getting tails on each toss:

[tex]P(TTT) = 0.5 \times 0.5 \times 0.5 = 0.125[/tex]

The probability of not getting three tails, which means getting at least one head in the three tosses, is the complement of getting all tails:

[tex]1 - P(TTT) = 1 - 0.125 = 0.875[/tex]

Thus, the probability of getting at least one head when a coin is tossed three times is [tex]0.875[/tex] or [tex]87.5\%[/tex].

This method can be useful in calculating probabilities using complements when it's easier to find the probability of the negative event (all tails) than to list all positive events (at least one head).

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