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Jeremiah makes 25% of the three-point shots he attempts. For a warm up, Jeremiah likes to shoot three-point
shots until he makes one. Let M be the number of shots it takes Jeremiah to make his first three-point shot.
Assume that the results of each shot are independent.
Find the probability that it takes Jeremiah fewer than 4 attempts to make his first shot.
You may round your answer to the nearest hundredth.
P(M < 4) =

Respuesta :

Cricetus

The probability will be "0.578".

Given values,

  • p = 25%

or,

          = 0.25

  • q = 1-p

           = 1-0.25

           = 0.75

To find the probability that it takes Jeremiah fever than 4 attempts is given by,

→ [tex]P(M<4) = P(1-P)^{M-1}[/tex]

M = 1, 2, 3

→                  [tex]= P[(1-P)^{1-1}+(1-P)^{2-1}+(1-P)^{3-1}][/tex]

→                  [tex]= P[1+(1-P)+(1-P)^2][/tex]

→                  [tex]= 0.25[1+0.75+0.75^2][/tex]

→                  [tex]= 0.25\times 2.3125[/tex]

→                  [tex]= 0.578125[/tex]

or,

→                  [tex]= 0.578[/tex]

Thus the above answer is right.    

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