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The probability that a coin will land heads up on any given toss is (1)/(2). If the coin is tossed three times, what is the probability that at least one of the tosses will land heads up?



Answer :

Answer:

the probability = 0.875

Step-by-step explanation:

We can find the probability that at least one of the tosses will land heads up by using the binomial distribution.

[tex]\boxed{P(x)=_nC_x\cdot p^x(1-p)^{n-x}}[/tex]

where:

  • [tex]P(x)=\texttt{probability of x successes}[/tex]
  • [tex]n=\texttt{number of trials}[/tex]
  • [tex]C=\texttt{combination}[/tex]
  • [tex]p=\texttt{success rate}[/tex]

Instead of adding the probabilities of 1 head, 2 heads and 3 heads. It will be easier to subtract the probability of 0 head with 1. Therefore:

[tex]P(\texttt{at least 1 head)}=1-P(0)[/tex]

Given:

  • [tex]n=3[/tex]
  • [tex]p=\frac{1}{2} =0.5[/tex]
  • [tex]x=0[/tex]

[tex]\begin{aligned}\\P(\texttt{at least q head})&=1-P(0)\\\\&=1-_3C_0\cdot (0.5)^0(1-0.5)^{3-0}\\\\&=1-\frac{3!}{0!(3-0)!} (1)(0.5)^3\\\\&=\bf 0.875\end{aligned}[/tex]

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