Question

3. Two different events can occur called A and B. The probability that A occurs is 0.90, the probability that B is 0.70, while the probability that both occur is 0.65. Are the two events independent? What is the probability that either of the events occurs? If B occurs, what is the probability that A will occur? Sixty four athletes are to compete for an Olympic event. How many distinct ways can the three medals, gold, silver, and bronze be awarded? (Hint: does order matter?) 4. Twenty students are to be assigned to three groups: two will contain five members and the remaining ten are in the third group. Each student can only serve on one committee. How many distinct ways can this be done? (Hint: does order matter? The binomial coefficient is used for two groups, for more than two groups use the multinomial formula.) 5.

Answer 1

3:

Here we have

P(A) = 0.90, P(B) = 0.70, P(A and B) = 0.65

Since P(A and B) is not equal to P(A)P(B) so A and B are not independent.

By the additional rule,

P(A or B) = P(A) + P(B) - P(A and B)= 0.9 +0.7 - 0.65 = 0.95

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P(A |B) = P(A and B) / P(B) = 0.65 / 0.70 = 0.9286

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4:

Gold medal can be awarded in 64 ways, silver in 63 ways and bronze is 62 ways so possible number of ways of awarding medal is

64 *63 * 62 = 249984

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5: