Random Selection By Coin Toss Probability Assignment

Assignment Task

1. A balanced dime is tossed three The possible outcomes can be represented as follows.

HHH HTH THH TTH

HHT HTT THT TTT

Here, for example, HHT means that the first two tosses come up heads and the third tails. Find the probability that

• Exactly two of the three tosses come up

• The last two tosses come up

• All three tosses come up the

• The second toss comes up

2. A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a It decides to make the selection randomly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner.

MS SM HM JM WM

MH SH HS JS WS

Here, for example, MS represents the outcome that Maria is appointed chairperson and Susan is appointed secretary. List the outcomes constituting each of the following four events.

A = event a male is appointed chairperson,

B = event Holly is appointed chairperson,

C = event Will is appointed secretary,

D = event only females are appointed.

2. Draw a normal curve. Write its equation. What are the properties of normal curve? Explain.

Explain left-tail, right tail and two-tailed test statement of hypothesis with the help of normal curve.

3. Discuss probability mass function.

MJ SJ HJ JH WH

MW SW HW JW WJ

The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its Web site. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 1981 to July 2000.

Crew size    2 3   4 5   6    7 8

Frequency   4   1   2 36 18 33 2

Let X denote the crew size of a randomly selected shuttle mission between April 1981 and July 2000.

• What are the possible values of the random variable X?
• Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of
• Find P(X = 4); interpret in terms of
• Obtain the probability distribution of X.
• Construct a probability histogram for X.
• What are the mean and variance of the random variable X?

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