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Chapter 15: Q7P (page 743)

What is the probability that the 2 and 3 of clubs are next to each other in a shuffled deck? Hint: Imagine the two cards accidentally stuck together and shuffled as one card.

Short Answer

Expert verified

Answer

The probability that the 2 and 3 of clubs are next to each other in a shuffled deck is 126

Step by step solution

01

Given Information

A deck of 52 cards is given.

02

Definition of Independent Event

When the order of arrangement is definite, the permutation is applied and when the order is not definite,combination is applied.

03

Finding the probability that the 2 and 3 of clubs are next to each other in a shuffled deck

Let the 2 and 3 of club stick together and is assumed to become a single card, this implies that the deck will have 51 cards. And the cards can be arranged inand the stuck cards can be arranged in.

The total arrangements possible is.

This implies that the number of outcomes favourable areand total number of outcomes are.

Apply the formula for probability, that isto get the probability that the 2 and 3 of clubs are next to each other in a shuffled deck.

Thus the required probability is.

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Most popular questions from this chapter

Suppose it is known that 1% of the population have a certain kind of cancer. It is also known that a test for this kind of cancer is positive in 99% of the people who have it but is also positive in 2% of the people who do not have it. What is the probability that a person who tests positive has cancer of this type?

Prove (3.1) for a nonuniform sample space. Hints: Remember that the probability of an event is the sum of the probabilities of the sample points favorable to it. Using Figure 3.1, let the points in A but not in AB have probabilities p1, p2, ... pn, the points in have probabilities pn+1, pn+2, .... + pn+k, and the points in B but not in AB have probabilities pn+k+1, pn+k+2, ....pn+k+l. Find each of the probabilities in (3.1) in terms of the 鈥檚 and show that you then have an identity.

Show thatP(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC).

Hint: Start with Figure 3.2 and sketch in a region C overlapping some of the pointsof each of the regions A, B, and AB.

Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use itto solve the problem. Use either a uniform or non-uniform sample space or try both.

You are trying to find instrument A in a laboratory. Unfortunately, someone has put both instruments A and another kind (which we shall call B) away in identical unmarked boxes mixed at random on a shelf. You know that the laboratory has 3 A鈥檚 and 7 B鈥檚. If you take down one box, what is the probability that you get an A? If it is a B and you put it on the table and take down another box, what is the probability that you get an A this time?

Show that if w=xyor,w=x/ythen(10.14) givesthe convenient formula for relative error

rww=(rxx)2+(ryy)2
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