Respuesta :
Solution:
Probability of a basketball player scoring on any shot = .75
Probability of a basketball player does not hit on the right point = 1-0.75=0.25
Probability that it will take her more than four shots to first scores on a shot = F F F F S +F F F F S S+ F F F F S S S+ F F F F S S S S F F F F S SS SS+...........
= F F F F S[1+S+S S+S S S+ S S S S+.......upto infinity]
= F F F F S [[tex]\frac{1}{1-S}[/tex]],→→→[ sum to infinity of a geometric progression a+a r+ a r²+ a r³,... .....= [[tex]\frac{a}{1-r}[/tex]], ]
= (0.25) × (0.25) ×(0.25)× (0.25)×(0.75)×[[tex]\frac{1}{0.25}[/tex]],
= 0.0625 × 0.25×0.75
=0.01171875
= 0.0118 (Approx)→→→→Option (d) is correct .
Answer:
Option a is correct that is .0156
Step-by-step explanation:
We have been given the probability of a basketball player scoring is p which is 0.75
So, q is 1-p
[tex]q=1-0.75=0.25[/tex]
Here, we need to find the probability that it will take her more than four shots
We will first find the shots for less than 4 in which we take cases for 1,2 and 3 shots.
We know that total probability is 1.
So, probability of more than four shots + probability of less than 4 shots =1
So, probability of less than 4 shots we will use binomial distribution which is
[tex]P(r)=^nC_r \cdotp^r\cdot q^{n-r}[/tex]
Here,n=3 and r will be 1,2 and 3 we will consider all three cases
We will add all three cases when r=1,2 and 3
[tex]^3C_1(.75)(.25)^2+^3C_2(.75)^2(.25)^1+^3C_3(.75)^3(.25)^0[/tex]
On simplification we will get:0.984375
Probability of three cases that is less than four shots is:=0.984375
So, the required probability is: 1-0.984375=0.015625
Therefore, Option a is correct.
