Question

27% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two (b) more than two (c) between two and five inclusive. If convenient, use technology to find the probabilities. (a) P(2)= (round to the nearest thousandth) (b) P(x>2)= (round to the nearest thousandth) (c) P (2 <= x <= 5)= (round to the nearest thousandth)

Answer 1

Answer:

a) P(2) = 0.2646

b) P(x > 2) = 0.5334

c) P( 2 <= x < = 5) = 0.7694

Step-by-step explanation:

n = 10

p = 0.27

q = 0.73

x = 10

P(x=0) = (10 C 0 )(0.27^0)(0.73^(10-0)) = 0.043

P(x=1) = (10 C 1 )(0.27^1)(0.73^(10-1)) = 0.159

P(x=2) = 0.2646

P(x=3) = 0.2609

P(x=4) = 0.1689

P(x=5) = 0.075

P(x=6) = 0.0231

P(x=7) = 0.0049

P(x=8) = 0.000677

P(x=9) = 0.0000557

P(x=10) =0.00000206

a) P(2) = 0.2646

b) P(x > 2) = P(3) + P(4) + P(5) + ... + P(10) = 0.5334

c) P( 2 <= x < = 5) = P(2) + P(3) + P(4) + P(5) = 0.7694

Answer 2

(a) Exactly two

P(2) = 0.2646

(b) More than two

P(x > 2) = P(3) + P(4) + P(5) + ... + P(10) = 0.5334

(c) Between two and five inclusive.

P( 2 <= x < = 5) = P(2) + P(3) + P(4) + P(5) = 0.7694

What is Probability?

Probability denotes possibility. It exists a branch of mathematics that deals with the happening of a random event. The value exists expressed from zero to one. Probability has been instructed in Maths to predict how likely events are to happen. The meaning of probability exists in the extent to which something is likely to happen.

Given,

n = 10

p = 0.27

q = 0.73

x = 10

P(x=0) = $(10C_0} )(0.27^0)(0.73^(10-0)) = 0.043$

P(x=1) = $(10C_{1} )(0.27^1)(0.73^(10-1)) = 0.159$

P(x=2) = 0.2646

P(x=3) = 0.2609

P(x=4) = 0.1689

P(x=5) = 0.075

P(x=6) = 0.0231

P(x=7) = 0.0049

P(x=8) = 0.000677

P(x=9) = 0.0000557

P(x=10) =0.00000206

(a) exactly two

P(2) = 0.2646

(b) more than two

P(x > 2) = P(3) + P(4) + P(5) + ... + P(10) = 0.5334

(c) between two and five inclusive.

P( 2 <= x < = 5) = P(2) + P(3) + P(4) + P(5) = 0.7694

To learn more about Probability refer to:

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