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Chapter 3: Q.3.38 (page 100)

Urn Ahas 5white and 7black balls. Urn Bhas 3white and 12black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

Short Answer

Expert verified

The probability that the coin landed tails is 1237.

Step by step solution

01

Given information

Urn Ahas 5white and 7black balls. Urn Bhas 3white and 12black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected.

02

Solution

Urn A5 white

7Black鈬�P(white)=512

Urn B3 White

12Black鈬�P(white)=315

P(Tail | white)=12脳31512脳315+12脳512

=330脳24074

=1237

03

Final answer

The probability that the coin landed tails is1237.

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Most popular questions from this chapter

The probability of getting ahead on a single toss of a coin is p

Suppose that Astarts and continues to flip the coin until a tail shows up, at which point Bstarts flipping.

Then Bcontinues to flip until a tail comes up, at which point Atakes over, and so on.

Let Pn,mdenote the probability that Aaccumulates a total of n heads before Baccumulates m

Show that

Pn,m=pPn-1,m+(1-p)1-Pm,n

In a certain village, it is traditional for the eldest son (or the older son in a two-son family) and his wife to be responsible for taking care of his parents as they age. In recent years, however, the women of this village, not wanting that responsibility, have not looked favorably upon marrying an eldest son.

(a) If every family in the village has two children, what proportion of all sons are older sons?

(b) If every family in the village has three children, what proportion of all sons are eldest sons?

Assume that each child is, independently, equally likely to be either a boy or a girl.

There are 3 coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

A coin having probability .8of landing on heads is flipped. A observes the result鈥攅ither heads or tails鈥攁nd rushes off to tell B. However, with probability .4, A will have forgotten the result by the time he reaches B. If A has forgotten, then, rather than admitting this to B, he is equally likely to tell Bthat the coin landed on heads or that it landed tails. (If he does remember, then he tells Bthe correct result.)

(a) What is the probability that B is told that the coin landed on heads?

(b) What is the probability that Bis told the correct result?

(c) Given that B is told that the coin landed on heads, what is the probability that it did in fact land on heads?

A couple has 2 children. What is the probability that both are girls if the older of the two is a girl ?
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