High School

What is the probability of getting at least 1 head on 4 successive tosses of a coin?

Group of answer choices:
1) 1/2 + 1/2 + 1/2 + 1/2
2) 1 – (1/2 + 1/2 + 1/2 + 1/2)
3) 1/2 x 1/2 x 1/2 x 1/2
4) 1 – (1/2 x 1/2 x 1/2 x 1/2)

Answer :

To find the probability of getting at least 1 head on 4 successive tosses of a coin, we can use the concept of complementary probability.

Step-by-Step Explanation:

  1. Understand the Problem:

    • We want at least 1 head in 4 coin tosses.
    • The complementary event is getting 0 heads in 4 coin tosses.

  2. Calculate the Probability of the Complementary Event:

    • Getting 0 heads means getting tails on all 4 tosses.
    • The probability of getting a tail on one toss is [tex]\frac{1}{2}[/tex].
    • Therefore, the probability of getting tails on 4 tosses is:
      [tex]\left( \frac{1}{2} \right)^4 = \frac{1}{16}[/tex]

  3. Calculate the Probability of Getting at Least 1 Head:

    • The probability of at least 1 head is the complement of getting 0 heads:
      [tex]1 - \frac{1}{16} = \frac{15}{16}[/tex]

From the given multiple-choice options, the correct choice is:

  1. [tex]1 - \left( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \right)[/tex]

This calculation demonstrates that the probability of getting at least 1 head in 4 successive tosses of a coin is [tex]\frac{15}{16}[/tex].

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