Respuesta :
a) 32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.
b) 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.
What is probability?
It is a branch of mathematics that deals with the occurrence of a random event.
Using Binomial distribution,
[tex]P(x) = C_{n , x} * p^{x}* (1-p)^ {n-x}[/tex]
We have, p= 0.52
A) probability that exactly 3 drivers text while driving if a police officer pulls over five drivers
[tex]P(x) = C_{5 , 3} * (0.52)^{3}* (0.48)^ {2}[/tex]
P(x) = 10* 0.140608* 0.2304
P(x)= 0.3239
32.4% probability that exactly 3 drivers text while driving if a police officer pulls over five drivers.
B) probability the next driver texting while driving that the police officer pulls over is the fifth driver
[tex]P(x) = C_{4 , 0} * (0.52)^{0}* (0.48)^ {4}[/tex]
P(x) = 1 * 1 * 0.053084
P(x) = 0.053084
So, 0.0531*0.52 = 0.0276
Hence, 2.76% probability the next driver texting while driving that the police officer pulls over is the fifth driver.
Learn more about binomial distribution here:
https://brainly.com/question/14565246
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