Question

Exercises For each of the following situations, discuss whether the term probability seems to be used correctly and, if so, how such a probability might have been determined. a A physician prescribes a medication for an infection but says that there is a probability of 0.2 that it will cause an upset stomach. b. An engineer who has worked on the development of a robot says that it should work correctly for at least 1,000 hours with probability 0.99. C. A friend says that the probability of extraterrestrial life is 0.1. 4.8 How good is your intuition about probability? Look at the following situations and answer the questions without making any calculations. Rely on your intuition, and see what happens. a. A six-sided balanced die has four sides colored green and two colored red. Three sequences of tosses resulted in the following: RGRRR RGRRRG GRRRRR Order the sequences from most likely to least likely b. If a balanced coin is tossed six times, which of die the following sequences is more likely. HTHTTH or HHHTTT? Which of the following is more likely, HTHTTH or HHHHTH?

Answer 1

4.7)

a)

The term probability seems to be used correctly.

Reason: Some medications have side effects and the probability of such effects are usually calculated by conducting trials on patients before the medicine sold/ prescribed to patients.

b)

The term probability seems to be used correctly.

Reason: The probability of failure of equipments within a period of time is called as reliability of an equipment. These are found out through testing of the equipment for a certain amount of time in labs.

c)

The term probability does not seem to be used correctly.

Reason: This statement is a guess or an intuition which is not based on the actual probability of an event happening.

4.8)

a.)

The correct order is

RGRRR

RGRRRG

GRRRRR

Reason: In the first sequence, there are only 5 trials compared to 6 in other sequences. So that sequence is more likely compared to other sequences. Among the 2nd and 3rd, Second sequence has 2 G compared to 1 G in 3rd sequence. SInce there are 4 Green sides, a sequence with 2 G has more probability.

b.)

Out of HTHTTH and HHHTTT, both are equally likely.As the coin is balanced any such sequence with equal number of tosses is equally likely.

Similarly, both HTHTTH and HHHHTH are equally likely. As the coin is balanced any such sequence with equal number of tosses is equally likely.