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Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 25% of the time, three events 25% of the time, two events 15% of the time, one event 5% of the time, and no events 5% of the time. (a) Find the probability that Javier volunteers for less than three events each month. P(X < 3)

Respuesta :

Answer:

The probability of Javier volunteers for less than three a month is 25%

Step-by-step explanation:

According to the questions,

The probability of Javier to attend exactly 5 events :-

P ( x = 5 ) = 25% = [tex]\frac{1}{4}[/tex]

The probability of Javier to attend exactly 4 events :-

P ( x = 4 ) = [tex]\frac{1}{4}[/tex]

The probability of Javier to attend exactly 3 events :-

P ( x = 3 ) = [tex]\frac{1}{4}[/tex]

The probability of Javier to attend exactly 2 events :-

P ( x = 2 ) = [tex]\frac{3}{20}[/tex]

The probability of Javier to attend exactly 1 events :-

P ( x = 1 ) = [tex]\frac{1}{20}[/tex]

The probability of Javier to attend no events :-

P ( x = 0 ) = [tex]\frac{1}{20}[/tex]

Now we have to calculate the probability of Javier volunteers for less than three P ( x < 3 ).

P ( x < 3 ) = P ( x = 0 ) + P ( x = 1 ) + P ( x = 2 )

P ( x < 3 ) = [tex]\frac{1}{20} + \frac{1}{20} + \frac{3}{20}[/tex]   [tex]= \frac{1 + 1 + 3}{20}[/tex]  = [tex]\frac{5}{20}[/tex]  = [tex]\frac{1}{4}[/tex]   = 0.25 = 25 %.

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