1. Calculate the probability of each of the following events. (4 points) At leas
ID: 3069237 • Letter: 1
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1. Calculate the probability of each of the following events. (4 points) At least one head comes up in a sequence of four flips of a coin For a die that is 3 times as likely to land on 1, 5, or 6 as it is to land on 2, 3, or 4, calculate the probability of rolling an odd number In a lottery where four digits are randomly selected with replacement and any permutation of the matching numbers means you win, find the probability of winning if you select the number 1, 1, 5, 0 In the same lottery as part c, suppose you instead select the number 3, 4, 5, 1. a. b. c. d. 2. Given P(A)0.4, P(B)0.5, and P(AUB) 0.7, find the following. (4 points) a. P(AnB) d. P(An B') 3. An automobile manufacturer is concerned about a possible recall of a certain car. For a recalled car, the following table gives the probability of a defect in certain parts of the car. (4 points) System/Area Probabilit Brake System Transmission Fuel System 0.25 0.18 0.17 0.40 Other Given that the probability of simultaneous defects in both the brakes and fuel system is What is the probability that there are no defects in either the brakes or the fuel system? Bean seeds from supplier A have an 85% germination rate and those from supplier B have a 75% a. 0.15, what is the probability of having a defect in either the brakes or the fuel system? b. 4. germination rate. A seed packaging company purchases 40% of their bean seeds from supplier A and 60% from supplier B then mixes those seeds together. (3 points) Find P(G), the probability that a randomly selected seed (from the mixed sees) will germinate Given that a seed germinates, find the probability that the seed was purchased from supplier A. Given that a seed does not germinate, find the probability that the seed was purchased from supplier A. a. b. c.Explanation / Answer
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2. P(a) = .4
P(b)= .5
P(a u b) = .7
1. P( a and B) = p(a)+p(b)--(a u b) = .4+.5-.7 = .2
2.p(a' u b') = 1-p(a u b ) = 1- .7 = .3
3. P(a' and B) = p( b only) = p(b)-p( and B)
= .5-.2
= .3
4. P( a and b')
= P( a only) = p(a)-( a and B)
= .4-.2
= .2
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