18. Two cards are selected in sequence from a standard 52-card deck. Find the probability that the second card is a six, given that the first card is a diamond. 19. One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral launch goes off on schedule. If A and B are independent events with P(A) > P(B), P(A U B) = 0.626, and P(A intersection B) = 0.144, determine the values of P(A) and P(B) to three decimal places. 20. The table below shows the number of male and female students enrolled in nursing at a university for a recent semester. a. Find the probability that a randomly selected student is a nursing major. b. Find the probability that a randomly selected student is male. c. Find the probability that a randomly selected student is a nursing major, given that the student is male. d. Find the probability that a randomly selected student is a nursing major and male. e. Are the events being a male student and being a nursing major independent or dependent events? .
18)
Case when first card diamond but not 6 = 12/52 * 4/51
Case when first card is diamond and 6 = 1/52 * 3/51
Required Probability = 12/52 * 4/51 + 1/52 * 3/51 = 0.019 Answer
19)
For indipendent events , P (A and B) = P(A)*P(B) = 0.144
or, P(A) = 0.144/P(B)
P(A U B) =P(A) + P(B) - P (A and B)
=>0.626 =P(A) + P(B) - 0.144
=> P(A) + P(B) = 0.77
=> 0.144/P(B) + P(B) = 0.77
=> P(B)^2 - 0.77P(B) + 0.144 =0
=>P(B) = 0.45 , 0.32
For, P(B) =0.45 ; P(A) = 0.144/0.45 = 0.320 -----------------> Not satisfies given condition P(A)>P(B)
For, P(B) =0.32 ; P(A) = 0.144/0.32 = 0.450 ------------------> Satisfies given condition P(A)>P(B)
Answer : P(A) = 0.450 ; P(B) = 0.320
20)
a) P = 1167 / 3964 = 0.294
b) P = 1255 / 3964 = 0.317
c) P = (151 / 3964) / (0.317) = 0.120
d) P = 151 / 3964 = 0.038
e) P1*P2 = (1255 / 3964) * (1167/3964) = 0.093
P1 and P2 = 0.038
Hence not independent
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