Help with statistics problem! thank you :)?

Question

1. Then probability that a student has a Visa card (V) is .70. The probability that a student has a MasterCard (M) is .60. The probability that a student has both cards is .50.

a. Find the probability that a student has either a Visa or a MasterCard.

b. Find the probability that a student who you know already has a MasterCard also has a Visa.

c. Find the probability that a student you know already has a Visa also has a MasterCard.

d. In this problem, are V and M independent? Explain.

2.Consider a population of 1,024 mutual funds that primarily invested in large companies. You determined that μ, the mean one-year total percentage return achieved by the funds, is 8.20 and that σ, the standard deviation, is 2.75. IN addition, suppose you determined that the range in the one year total returns is from -2.0 to 17.1 and that the quartiles are, respectively, 5.5 (Q1) and 10.5 (Q3). According to the empirical rule, what percentages of these funds is expected to be

a. within +/-1 standard deviation?

b. within +/- 2 standard deviations of the mean?

c. According to Cebyshev’sule what percentage of these funds are expected to be within +/- 1, +/- 2 or +/- 3 standard deviations?

d. According to Chebyshevs rule, at least 93.75% of these funds is expected to have one-year total returns between what two amounts?

Answer 1

1.(a).

P(Visa or Mastercard)

= P(Visa) + P(Mastercard) - P(visa and Mastercard)

= 0.70 + 0.60 - 0.50

= 0.80

1(b).

P(Visa/Mastercard)

= P(visa and Mastercard)/ P(Mastercard)

= 0.50/0.60

= 5/6

= 0.83

1(c).

P(Mastercard/Visa)

= P(visa and Mastercard)/ P(Visa)

= 0.50/0.70

= 5/7

= 0.714285714

1(d).

P(Visa)* P(Mastercard)

= 0.70* 0.60

= 0.42

P(visa and Mastercard)

= 0.50

Since P(Visa)* P(Mastercard)≠ P(Visa and Mastercard)

i.e. 0.42≠0.50,

Therefore, V and M are NOT independent.