GATE (GA) Textile 2016 Question Paper Solution | GATE/2016/GA/09

Question 09 (General Aptitude)

Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

(A)	0.2508
(B)	0.2816
(C)	0.2934
(D)	0.6000

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By poisson distribution-
Probability , $P=\frac{e^-\lambda \times (\lambda^r)}{r!}$
Where, $\lambda=np$
p=60/100=0.6
n=10
$\lambda=10\times 0.6$
$\lambda=6$
r=6
By putting these values in the formula, we get-
Probability , $P=\frac {e^-6 \times (6^6)}{6!}$
Probability , $P=\frac{403.42 \times (46656)}{6\times 5\times 4\times 3\times 2\times 1}$
Probability , $P=\frac{403.42 \times (46656)}{720}$
P=0.2508 (Ans)