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An ordinary deck of playing cards has 52 cards. Three are four suits_ spade heart , diamond and club with 13 card in each suit. Spade and clubs are black heart and diamond are red. One of these cards is selected at random. Let R denote the event that a red is chosen . Find the probability that a red card is chosen, and express your answer in probability that a red card is chosen and express your answer in probability natation

A bowl contains 12 poker chips 3 red , 4 white and 5 blue. One of these poker chips is selected at random from the bowl. Let B denote the event that the chips is selected is blue. Find the probability that a blue chips is selected, and express your answer in probability notation

Suppose that C and D are mutually exclusive events such that $P\left(C\right)=0.14$and$P\left(D\right)=0.32$ Determine $P(CorD)$.

Interpret each of the following probability statements, using the frequentist interpretation of probability.

(a). The probability is 0.487 that a newborn baby will be a girl.

(b). The probability of a single ticket winning a prize in the Powerball lottery is 0.031.

Suppose that A and B are events such that $P\left(A\right)=\frac{1}{4}$,$P\left(B\right)=\frac{1}{3}$and $P(AorB)=\frac{1}{2}$

Part (a). Are event A and B mutually exclusive ? Explain your answer.

Part (b) Find$P(A\&B)$

Age and senators. According to the congressional directory, the official directory of the U.S Congress prepared by the Joint Committee on printing the age distribution for senators in the U.S Congress as of fall 2013, is as shown in the following table.

Suppose that a U.S senator is selected at random. let

A = event the senator is under 50,

B = event the senator is in his or her 50s,

C = event the senator is in his or her 60s, and

S = event the senator is under 70.

Part (a) Use the table and the f/N rule to find P(S).

Part (b) Express event S in term of event A,B and C

Part (c) Determine P(A), P(B) and P(C).

Part(d) Compute P(S), Using the special addition rule and your answers from part (b) and part(c) Compare your answer with in parts (a)

Sample Size for Proportion Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage.