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In: Statistics and Probability

When we toss a penny, experience shows that the probability (longterm proportion) of a head is...

When we toss a penny, experience shows that the probability (longterm proportion) of a head is close to 1-in-2. Suppose now that we toss the penny repeatedly until we get a head. What is the probability that the first head comes up in an odd number of tosses (one, three, five, and so on)? To find out, repeat this experiment 50 times, and keep a record of the number of tosses needed to get a head on each of your 50 trials.

(a)

From your experiment, estimate the probability of a head on the first toss. What value should we expect this probability to have?

b)

Use the expected value to estimate the probability that the first head appears on an odd-numbered toss.

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Expert Solution

Answer:-

Given That:-

When we toss a penny, experience shows that the probability (longterm proportion) of a head is close to 1-in-2. Suppose now that we toss the penny repeatedly until we get a head. What is the probability that the first head comes up in an odd number of tosses (one, three, five, and so on)? To find out, repeat this experiment 50 times, and keep a record of the number of tosses needed to get a head on each of your 50 trials.

(a) From your experiment, estimate the probability of a head on the first toss. What value should we expect this probability to have?

The probability of a head on the first toss = 1/2

b) Use the expected value to estimate the probability that the first head appears on an odd-numbered toss.

The probability of a head appears on an odd-numbered toss = 0.5 + (0.5)3 +(0.5)5 + ---------

= 0.5 [1 + (0.5)2 + (0.5)4 + - - - - - -]

= 0.5

= 0.5 [4/3]

= 2/3

The probability of a head appears on an odd-numbered toss = 0.67

Plz like it....,

orchestra answered 1 year ago
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