Stat1000W12_A4_sols

Stat1000W12_A4_sols - STAT 1000 Assignment 4 – REVISED...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 1000 Assignment 4 – REVISED DUE: March 14th (Wed. Eve. Section), March 15th (T/Th. Sections), March 16th (MWF. Sections) SHOW ALL YOUR WORK 1. [5] Suppose we have the following information about credit card ownership for Canadian adults: • 51% have a Mastercard (M) • 20% have an American Express card (A) • 70% have a Visa (V) • 29% have a Visa and a Mastercard • 14% have a Visa and an American Express card • 8% have a Mastercard and an American Express card • 6% have all three cards (a) If we randomly select one Canadian adult, what is the probability they have a Mastercard or a Visa? Solution: P(M or V) = P(M) + P(V) - P(M and V) P(M or V) = 0 . 51 + 0 . 70- . 29 = 0 . 92 (b) If we randomly select one Canadian adult, what is the probability that he or she has a Mastercard or an American Express, but not both? Solution: P(M or A) = P(M) + P(A) - P(M and A) P(M or A) = 0 . 51 + 0 . 20- . 08 = 0 . 63 Since we are looking for an individual who has either card but not both, 0 . 63- . 08 = 0 . 55 (c) What is the probability that a randomly selected Canadian adult has a Visa and no Mastercard? Solution: The easiest way to see this is by looking at the Venn diagram, "#$% %&'(#)%* '+,('$$ &%$-'()%(. /01/ /023 /04/ /015 /0/6 /037 /0/8 P(V) - P(V and M) . 70- . 29 = 0 . 41 (d) Are any two of the three events independent of one another? Explain? Solution: Two events are independent if and only if; P(A and B) = P(A)P(B) P(M and A) 6 = P(M)P(A) . 08 6 = (0 . 51)(0 . 20) . 08 6 = 0 . 10 Therefore, Mastercard and American Express are not independent. P(V and A) = P(V)P(A) . 14 = (0 . 70)(0 . 20) . 14 = 0 . 14 Therefore, Visa and American Express are independent. P(M and V) 6 = P(M)P(V) . 29 6 = (0 . 51)(0 . 70) . 29 6 = 0 . 357 Therefore, Mastercard and Visa are not independent. 2. [5] A baseball player compiles the following information: • He hits a homerun (H) in 34% of his games. • He gets a strikeout (S) in 40% of his games. • In 78% of his games, he hits a home run or his team wins (W). • In 10% of his games, he hits a home run and gets a strikeout. • In 26% of his games, he hits a home run and his team wins. • In 28% of his games, he gets a strikeout and his team wins. (a) In any given game, what is P(H or S)? Solution: P ( H or S ) = P ( H ) + P ( S )- P ( H and S ) = 0 . 34 + 0 . 40- . 10 = 0 . 64. (b) What is P(W)? Solution: We know P ( H or W ) = P ( H ) + P ( W )- P ( H and W ) ⇒ P ( W ) = P ( H or W )- P ( H ) + P ( H and W ) = 0 . 78- . 34 + 0 . 26 = 0 . 70. (c) What is P(H and W c )? Solution: The probability that the player gets a homerun is equal to the probability that he gets a homerun and the team wins, plus the probability that he gets a homerun and his team doesn’t win, i. e....
View Full Document

{[ snackBarMessage ]}

Page1 / 10

Stat1000W12_A4_sols - STAT 1000 Assignment 4 – REVISED...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online