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if the probability of an airplane flight arrives on time is 0.75 find the probability that 2 out of 3 will all arrive on time.

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ANSWER

[tex]P(\frac{2}{3})=0.14[/tex]

EXPLANATION

The probability that a plane will arrive on time is:

[tex]P(on-time)=0.75[/tex]

This means that the probability that a plane will not arrive on time is:

[tex]\begin{gathered} P(not-on-time)=1-0.75 \\ P(not-on-time)=0.25 \end{gathered}[/tex]

The probability that 2 out of 3 planes will arrive on time is the probability that 2 planes will arrive on time and that one will not arrive on time.

Therefore, we have to find the product of each probability:

[tex]\begin{gathered} P(\frac{2}{3})=0.75\cdot0.75\cdot0.25 \\ P(\frac{2}{3})=0.14 \end{gathered}[/tex]

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