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If 50 tickets are sold and 2 prizes are to be awarded, find the probability that

ID: 3181929 • Letter: I

Question

If 50 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets. Find the probability of getting a full house (3 cards of one denomination and 2 of another) when 5 cards are dealt from an ordinary deck. Encyclopedia Britannica's list of 20 World Class Orchestras includes the following from the United States: Boston Symphony Orchestra, Chicago Symphony Orchestra, Cleveland Orchestra, Los Angeles Philharmonic. New York Philharmonic. Philadelphia Orchestra, and the San Francisco Symphony. Choose 5 at random from the list of 20 for a benefit CD. What is the probability that the collection will include at least one group from the United States? At least 2 from the United States? That all 5 will be from the United States? The red face cards and the black cards numbered 2-9 are put into a bag. Four cards are drawn at random without replacement. Find the following probabilities. All 4 cards are red. 2 cards are red and 2 cards are black. At least 1 of the cards is red. All 4 cards are black.

Explanation / Answer

Solution:-

Question 8)

Probability of getting a full house = 0.001441

This hand has the pattern AAABB where A and B are from distinct kinds.

The number of such hands = 13C1 × 4C3 × 12C1 × 4C2. = 3774

Total number of combinations of different hands = 52C5 = 2,598,960

Probability of getting a full house = 3774/2,598,960 = 0.001441.

Question 9)

p = 7/20 = 0.35

a) The probability that atleast one group from U.S is P(x > 1) = 0.88397

p = 0.35, n = 5, x = 1

By applying binomial distribution :-

P(x, n, p) = nCx*px*(1 - p)(n -x )

P(x > 1) = 0.88397

b) The probability that atleast two group from U.S is 0.5716.

p = 0.35, n = 5, x = 2

By applying binomial distribution :-

P(x, n, p) = nCx*px*(1 - p)(n -x )

P(x > 2) = 0.5716

c) The probability that 5 group from U.S is 0.005252

p = 0.35, n = 5, x = 5

By applying binomial distribution :-

P(x, n, p) = nCx*px*(1 - p)(n -x )

P(x = 5) = 0.005252