Question

It is known that a certain basketball player will successfully make a free throw 87.4% of the time. Suppose that the basketball player attempts to make 14 free throws. What is the probability that the basketball player will make at least 11 free throws?

  

Let XX be the random variable which denotes the number of free throws that are made by the basketball player. Find the expected value and standard deviation of the random variable.

  E(X)=
   σ=

Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace the card, and draw another card. You repeat this process until you have drawn 16 cards in all. What is the probability of drawing at least 7 spades?

  

For the experiment above, let XX denote the number of spades that are drawn. For this random variable, find its expected value and standard deviation.

E(X)=
   σ=

Answer 1

solution 1:

probability of making a free throw = p = 87.4% = 0.874

number of attempts = n = 14

we have to find the probability of atleaast 11 throws =

= P(X=11)+P(X=12) + P(X= 13) + P(X= 14)

using formula of binomial distribution

= 0.16552 + 0.28702 + 0.3063 + 0.15176 = 0.9106

b)

expected value E(x) = n*p = 14*0.874 = 12.236

solution : 2)

total number of cards in deck = 52

total option to draw a spade = 13

so probability of drawing a spade = p = 13/52 = 0.25

number of trial 16

we have to find the probability of drawing atleast 7 spades =

since the probability of drawing card in every trial is independent becarse first drawn card are replaced,

so we can use binomial formula

= 1 - P(X < 7)

P(X < 7) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X+5)+P(X=6)

P(X < 7) = 0.01002 +0.05345 + 0.13363 + 0.20788 + 0.2252 + 0.18016 + 0.1101 = 0.92042

= 1 - 0.92042 = 0.0796

b)

expected value = E(X) = n*p = 0.25*16 = 4

c)